We study an asymptotic Dirichlet problem for Weyl structures on asymptotically hyperbolic manifolds. By the bulk-boundary correspondence, or more precisely by the Fefferman-Graham theorem on Poincaré metrics, this leads to a natural extension of the notion of Branson's -curvature to Weyl structures on even-dimension…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Weyl asymptotics”
The paper examines the smoothness of hyperbolic metrics near boundaries.
problem Analyzing the regularity of asymptotically hyperbolic metrics near boundaries.
method Following Michael Anderson's method, the paper studies conformally compact Riemannian metrics with Einstein equation.
result The conformal compactifications of these metrics are up to the boundary when Weyl curvature is in and the boundary metric is in .
Proves Weyl's law for metric spaces with Ricci curvature.
problem Proving Weyl's law for metric measure spaces with bounded Ricci curvature.
method Analyzes spaces to prove asymptotic eigenvalue formula.
result Establishes Weyl's law for Dirichlet eigenvalues in metric measure spaces.
In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of biharmonic Stekloff eigenvalues with Neumann boundary condition in a bounded domain of an -dimensional Riemannian manifold.
Researchers prove Weyl laws for Schrödinger operators on noncompact manifolds.
problem Proving Weyl laws for Schrödinger operators on noncompact manifolds.
method Heat kernel asymptotics, Karamata-Hardy-Littlewood Tauberian theorem, and semiclassical analysis.
result Established both classical and semiclassical Weyl laws for Schrödinger operators on noncompact manifolds.
Study spectral properties of sub-Riemannian Laplacians, proving quantum ergodicity and heat kernel asymptotics.
problem Spectral properties of sub-Riemannian Laplacians.
method Quantum ergodicity results, small-time asymptotics of sub-Riemannian heat kernels, Weyl law.
result Weyl law and spectral concentration on Lie brackets of length r-1.
Improved remainder estimate for eigenvalue asymptotics on manifolds with group actions.
problem Asymptotic distribution of eigenvalues of invariant elliptic operators.
method Refined stationary phase approximation and singular critical sets analysis.
result Asymptotic multiplicity formula for families of irreducible representations.
We discuss asymptotic behavior of the eigenvalue distribution of the differential form Laplacian on a Riemannian foliated manifold when the metric on the ambient manifold is blown up in directions normal to the leaves (in the adiabatic limit). Motivated by analogies with semiclassical spectral asymptotics, we use ideas…
Motivated by recent interest in the spectrum of the Laplacian of incomplete surfaces with isolated conical singularities, we consider more general incomplete m-dimensional manifolds with singularities on sets of codimension at least 2. With certain restrictions on the metric, we establish that the spectrum is discrete …
Symmetries of Einstein-Weyl manifolds can be extended from boundary surfaces.
problem Extending symmetries from boundary surfaces to Einstein-Weyl manifolds.
method Starting from a symmetry of conformal Cartan connection on a boundary surface, proving symmetries can be extended.
result Symmetries of conformal Cartan connection on the boundary can be extended to symmetries of the Einstein-Weyl manifold.
Researchers study eigenvalues on singular Riemannian manifolds, showing how curvature affects Weyl's law.
problem Analyzing eigenvalues of Laplace-Beltrami operator on singular Riemannian manifolds with unbounded geometrical invariants.
method Developed a new quantitative estimate for the remainder of the heat trace and Weyl's function on Riemannian manifolds.
result Constructed singular Riemannian metrics with prescribed non-classical Weyl's law for various slowly varying functions.
On the asymptotic behavior of Einstein manifolds with an integral bound on the Weyl curvaturemath.DG
In this paper we consider the geometric behavior near infinity of some Einstein manifolds with Weyl curvature belonging to a certain space. Namely, we show that if , , admits an essential set and has its Weyl curvature in for some , then must be a…
The study shows how geometric Weyl bulk-density exponent rigidifies spectral encodings in O-regularly varying classes.
problem Understanding spectral encodings under Weyl growth conditions.
method Analyzing geometric Weyl bulk-density exponent and proving spectral rigidity.
result The geometric Weyl bulk-density exponent rigidifies spectral encodings in the O-regularly varying class, leading to unique admissible exponents and scaling laws.
Starting from a real analytic conformal Cartan connection on a real analytic surface , we construct a complex surface containing a family of pairs of projective lines. Using the structure on we also construct a complex -space , such that is a twistor space of a self-dual conformal -fold and …
Tubes in sub-Riemannian geometry and a Weyl's invariance result for curves in the Heisenberg groupsmath.DG
The paper studies sub-Riemannian geometry and proves a Weyl's invariance result for Heisenberg groups.
problem Optimal regularity and volume asymptotics of submanifolds in sub-Riemannian structures.
method Analyzes tubular neighborhoods and uses Weyl's invariance for Heisenberg groups.
result Volume of small tubes around curves in Heisenberg groups is invariant to embedding.
We prove an off-diagonal expansion for a Toeplitz operator with an indicator function.
problem Asymptotics of Toeplitz operators with indicator function
method Off-diagonal expansion
result We extend two results to the non-compact setting.
New stability and isolation results for Einstein manifolds.
problem Stability and isolation of Einstein manifolds.
method Conditions on Weyl tensor for AH and ALE manifolds, Bochner tensor for Kähler and Sasaki manifolds.
result Established new stability criteria and isolation results for various types of Einstein manifolds.
The paper defines curvature at infinity for flat manifolds.
problem Defining curvature at the boundary of flat manifolds.
method Constructing coordinates at infinity for asymptotically flat ends.
result A Weyl tensor and renormalized volume defined at infinity.
We prove the analogue of Weyl's law for a noncommutative Riemannian manifold, namely the noncommutative two torus equipped with a general translation invariant conformal structure and a Weyl conformal factor. This is achieved by studying the asymptotic distribution of the eigenvalues of the perturbed L…
New criterion for Weyl law on Riemannian manifolds without standard assumptions.
problem Establishing Weyl law for Schrödinger operators on complete Riemannian manifolds.
method Identifying a geometric-analytic invariant that balances manifold geometry, potential growth, and oscillation scale.
result Weyl asymptotic holds if approaches 0 as λ goes to infinity.
Generic density of equivariant min-max hypersurfaces in Riemannian manifolds.
problem Finding generic density of equivariant min-max hypersurfaces in Riemannian manifolds.
method Weyl asymptotic law for -equivariant volume spectrum, generic density result.
result Generic density of equivariant min-max hypersurfaces in Riemannian manifolds.
Combines noncommutative geometry and spectral theory for new Weyl laws.
problem Developing new Weyl laws for noncommutative manifolds.
method Functional analysis, spectral theory, and Tauberian conditions.
result Generalizes and simplifies recent results on Weyl laws and integration formulas.
We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped product type. Our main result is an upper bound on the resonance counting function with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base manifold defining the ends.
Refined asymptotics of scalar-flat ALE four-manifolds
problem Asymptotic behavior of scalar-flat ALE four-manifolds
method Constructing preferred coordinates at infinity
result Identifying homogeneous term in metric expansion
We obtain an estimate from below for the remainder in Weyl's law on negatively curved surfaces. In the constant curvature case, such a bound was proved independently by Hejhal and Randol in 1976 using the Selberg zeta function techniques. Our approach works in arbitrary negative curvature, and is based on wave trace as…
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the D…
The paper extends Weyl's law to CROSSes, showing sharpness and polynomial improvement.
problem Understanding the error term in Weyl's law for different types of manifolds.
method Analyzing the Laplacian eigenvalues on Compact Rank One Symmetric Spaces (CROSSes).
result For CROSSes, the error term in Weyl's law is sharp, and for products of CROSSes, it can be polynomially improved.
The study improves bounds on the number of closed geodesics and logarithmic improvements in the Weyl law.
problem Estimating the number of closed geodesics and improving logarithmic bounds in the Weyl law.
method Study of non-degeneracy properties of nearly closed orbits for predominant sets of metrics.
result Logarithmic improvements in the Weyl law and exponential bounds on the number of closed geodesics.
The Planck mass can be derived from gravitational potential behavior in compactifications.
problem Deriving the Planck mass from gravitational potential behavior in compactifications.
method Physical considerations and Weyl law application to gravitational potential behavior.
result The Planck mass can be reconstructed from the asymptotics of the masses of spin 2 Kaluza--Klein modes.
Eigenvalue distribution in gaps of the essential spectrum of the Bochner-Schrödinger operatormath.SP
The paper studies eigenvalues in gaps of the essential spectrum of a Bochner-Schrödinger operator.
problem Eigenvalue distribution in gaps of the essential spectrum of the Bochner-Schrödinger operator.
method Trace asymptotics formula and Weyl type asymptotic formula for eigenvalue counting function.
result The spectrum of in the gap is discrete.
Study heat traces for drifting Laplacian and Schrödinger operators on manifolds.
problem Analyzing heat traces for drifting Laplacian and Schrödinger operators on manifolds.
method Proved asymptotic expansions and remainder estimates for heat traces under different regularity conditions.
result The asymptotic behavior of the remainder is determined by higher regularity of the potential or weight function.
Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundarymath.DG
Study finds eigenvalue patterns on rough manifolds with measurable metrics.
problem Eigenvalue patterns on rough Riemannian manifolds with measurable metrics.
method Demonstrated a Weyl law for eigenvalues of Laplacian and weighted Laplace equations.
result Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds.
Mathematical counterparts to effective degrees of freedom inspired by Guth's results.
problem Understanding effective degrees of freedom in mathematical contexts.
method Formulating specific questions inspired by Guth's results and Weyl asymptotics.
result New mathematical counterparts to effective degrees of freedom.
The paper develops a heat kernel expansion for Rockland operators on filtered manifolds.
problem Analyzing heat kernel expansions for non-commutative geometries.
method Established a universal heat kernel expansion for Rockland operators on closed filtered manifolds using a new calculus.
result Implications of the heat expansion for complex powers, heat trace asymptotics, and eigenvalue asymptotics are generalized to this new calculus.
The study reveals scaling limits of spectral projectors on Riemannian manifolds.
problem Understanding spectral function scaling limits on Riemannian manifolds.
method New off-diagonal estimates and Weyl law application.
result Scaling limit of spectral projector is a normalized Bessel function.
Study spectral properties of curl operator on odd-dimensional manifolds.
problem Spectral analysis of curl operator on odd-dimensional manifolds.
method Computational and analytical methods including Weyl asymptotics and zeta-function analysis.
result Sharp lower eigenvalue bound for positively curved manifolds and detailed spectrum computations for specific manifolds.
We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants. The proof relies on a combinatorial interpretation of a recursive formul…
A note on the classification of four-dimensional gradient steady and expanding Ricci solitonsmath.DG
Study classifies 4D Ricci solitons with specific curvature conditions.
problem Classifying 4D gradient steady and expanding Ricci solitons with given curvature properties.
method Asymptotically cylindrical and conical assumptions; half-harmonic and half-nonnegative isotropic curvature conditions.
result Partial classification of 4D gradient expanding Ricci solitons with half-nonnegative isotropic curvature.
The paper broadens the class of manifolds where Dirac operator spectra are maximal.
problem Finding new manifolds with maximal Dirac operator spectra.
method Analyzing -spectrum, using sufficient conditions, and applying the Weyl criterion.
result New classes of manifolds with maximal Dirac operator spectra are identified.
Study on mode stability of gravitational instantons of type D.
problem Proving mode stability of gravitational instantons of type D.
method Analogous to Lorentzian case, analyze Weyl curvature scalars satisfying a separable Teukolsky equation.
result Prove mode stability, showing no solutions compatible with regularity and asymptotic flatness.
Study of 3d-3d correspondence involving -Weyl algebra and 3d-index.
problem Understanding the action of a -Weyl algebra on the 3d-index of knots.
method Investigation of the -Weyl algebra's module action on the 3d-index, conjecturing structural properties.
result Bilinear factorization, pair of linear -difference equations, and rational function matrix for the 3d-index determination.
Nahm Poles and 0-Instantonsmath.DG
Study of 0-instantons on hyperbolic manifolds, proving invariants and energy formulas.
problem Understanding 0-instantons on hyperbolic manifolds and their properties.
method Analyzing asymptotic expansions and using Fefferman-Graham expansion for Poincaré-Einstein metrics.
result The 0-instanton obstruction tensor is a conformal invariant related to Weyl curvature, vanishing for smooth 0-instantons.
Researchers found a Weyl law for Liouville quantum gravity eigenvalues.
problem Understanding the spectral geometry of Liouville quantum gravity.
method Obtained a Weyl law for eigenvalues of Liouville Brownian motion.
result The -th eigenvalue grows linearly with , with a constant determined by the Liouville area and a specific .
Study local Weyl law on hyperbolic surfaces, identifying geodesic loops.
problem Understanding the variance of a local Weyl law on hyperbolic surfaces.
method Explicit integration of test functions, stationary phase arguments, and geometric analysis of geodesic loops.
result Identifies length-minimizing geodesic loops and sequences, proving they are simple.
The study of the spectrum of the Laplacian on forms over manifolds.
problem Analyzing the spectrum of the Laplacian on forms over manifolds with specific curvature properties.
method Generalization of Weyl's criterion, Cheeger-Fukaya-Gromov theory, and continuous perturbations of the operator.
result Significantly stronger results for the spectrum of the Laplacian on forms, including its behavior under metric deformations.
In the first part of this article we revisit the theory of weighted spinors on conformal manifolds. In the second part we introduce the notions of asymptotically flat Weyl structures and of associated mass, and we prove a conformal version of the positive mass theorem on conformal spin manifolds.
The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.
problem Determining if a spacetime is conformally AdS based on null geodesic travel times.
method Analyzing all null geodesics from a point to its antipodal point, considering various spacetime conditions.
result The spacetime is conformally AdS if and only if all null geodesics from a point refocus at its antipodal point.
This paper completes the classification of S1-symmetric static vacuum black holes.
problem Identifying all S1-symmetric static vacuum black hole solutions.
method Analyzing and constructing known solutions and proving their completeness.
result Proves that the Schwarzschild, Boost, and Weyl-Korotkin-Nicolai families exhaust all S1-symmetric static vacuum black hole solutions.