Derives an integral formula for G2-structures.
problem Calculating properties of G2-structures.
method Applies an integral formula for G-structures to G2.
result Derives an integral formula relating curvatures and quadratic invariants.
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.
168,657 papers · 148 categories
Trend · papers per month
48 results for “integral formulas”
Derives integral formulae on weighted manifolds.
problem No specific problem stated; focuses on mathematical derivations.
method Introduces weighted mean sigma-r curvature and uses weighted Newton transformations.
result Derives integral formulae generalizing previous work.
Mathematical formulas for elliptic curve integrals solve anomaly equations.
problem Mathematical formulation of contact term singularities on elliptic curves.
method Residue formulas and holomorphic anomaly equations.
result Regularized integrals on elliptic curves satisfy holomorphic anomaly equations.
Formula connects foliated simplicial volume with group cost.
problem Calculating integral foliated simplicial volume.
method Ergodic decomposition formula for simplicial volume.
result Integration formula linking foliated simplicial volume and group cost.
Integral formulas for a Riemannian manifold with several orthogonal complementary distributionsmath.DG
The paper proves integral formulas for manifolds with multiple orthogonal distributions.
problem Understanding geometric properties of manifolds with multiple orthogonal distributions.
method Develops integral formulas for Riemannian manifolds with orthogonal complementary distributions.
result Generalizes known formulas for and applies to manifold splitting and immersions.
The paper studies integral formulas for a specific type of soliton.
problem Integral formulas for compact gradient h-almost Ricci-Bourguignon solitons.
method Investigation of integral formulas and proving properties of solitons.
result Compact, non-trivial h-almost Ricci-Bourguignon solitons are isometric to a Euclidean sphere under certain conditions.
Exact formulas for volumes of specific knot cone-manifolds.
problem Finding exact volumes of cone-manifolds with two-bridge knots.
method Provided exact integral formulas using Chebyshev polynomials and algebraic equations.
result Exact formulas for hyperbolic and spherical volumes of cone-manifolds.
In this paper, we shall give an explicit Gauss diagram formula for the Kontsevich integral of links up to degree four. This practical formula enables us to actually compute the Kontsevich integral in a combinatorial way.
The article proves integral formulas for foliated sub-Riemannian manifolds.
problem Integral formulas for foliated sub-Riemannian manifolds.
method Proved a series of integral formulae involving mean curvatures, Newton transformations, and curvature tensor.
result Generalized known integral formulas for codimension-one foliations.
The article derives integral formulas for foliated sub-Riemannian manifolds.
problem Integrating geometric concepts in Riemannian manifolds with foliations.
method Deriving integral formulas involving shape operators and curvature tensor.
result Generalizes results for foliated Riemannian manifolds and includes arbitrary functions.
We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. As well we establish some upper and lower bounds …
Researchers confirm integral formulas for -structures in detail.
problem Verifying integral formulas for -structures on Riemannian manifolds.
method Detailed analysis and explicit expressions of intrinsic torsion using exterior algebra.
result Agreement of integral formulas with intrinsic torsion components.
We show that integration over a -manifold can be reduced to integration over a minimal section with respect to an induced weighted measure and integration over a homogeneous space . We relate our formula to integration formulae for polar actions and calculate some weight functions. In case of a compact …
Computing the Hopf invariantmath.CO
Algorithm calculates Hopf invariant for simplicial mappings.
problem Computing Hopf invariant for simplicial mappings.
method Proposed an algorithm based on Whitehead's integral formula.
result Algorithm successfully computes Hopf invariant.
Paper derives a Reilly type integral formula and applies it to inequalities and eigenvalue problems.
problem Developing a new integral formula and its applications in geometric inequalities and eigenvalue problems.
method Derives a Reilly type integral formula associated with the -Laplacian and applies it to inequalities and eigenvalue problems.
result Obtains Heintze-Karcher and Minkowski type inequalities, and eigenvalue relationships.
Sharp upper bounds derived for Alexandrov-Fenchel deficit using weighted Minkowski integral formulas.
problem Deriving upper bounds for the Alexandrov-Fenchel deficit.
method Using weighted Minkowski integral formulas and an integral formula for the deficit in Jensen's inequality.
result Quantitative estimates under weaker convexity assumptions, including a distance term.
Formula for integrating random variables on hyperbolic surfaces.
problem Integrating random variables on the moduli space of hyperbolic surfaces.
method Integration formula for lengths of closed geodesics.
result Integral of geometric random variables can be expressed as an integral over R.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
problem Proving a special case of the Gaussian kinematic formula.
method Viewing the GKF as the limit of spherical kinematic formulas for large dimension spheres.
result Proves a special case of the Gaussian kinematic formula.
New Crofton formulae derived from existing ones.
problem Generalizing Crofton formulae for products.
method Calculations in the ring of normal densities.
result Generalizations of Crofton formulae in terms of mixed Riemannian volume.
Formula connects curvature to volume in special geometric spaces.
problem Deriving formulas for curvature in specific geometric spaces.
method Used strong locality of Laplacian and eigenfunction approximation.
result Proved integral type Gauss-Green formula linking curvature to volume.
New formulas for measuring geometric properties of definable sets.
problem Measuring geometric properties of definable sets in a non-standard setting.
method Proved two kinematic formulas integrating on .
result Generalized Cauchy-Crofton and infinitesimal linear kinematic formulas.
We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce concrete integrations of several geometric stuctures defined infinitesimally. I…
The first author conjectured certain relations for Morita-Mumford classes and Newton classes in the integral cohomology of mapping class groups (integral Riemann-Roch formulae). In this paper, the conjecture is verified for cyclic subgroups of mapping class groups.
Integral formulas for a metric-affine manifold with two complementary orthogonal distributionsmath.DG
We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability tensors of the distributions. The formulas under some conditions yield splitting…
Integral formulae for foliated Riemannian manifolds provide obstructions for existence of foliations or compact leaves of them with given geometric properties. Recently, we associated a new Riemannian metric to a codimension-one foliated Finsler space and proved integral formulae for general and for Randers spaces. In …
Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.
problem Deriving and generalizing the Selberg trace formula.
method Supersymmetric localization principle and path integral derivation.
result Derives Selberg trace formula on arbitrary compact Riemann surfaces and generic compact locally symmetric spaces.
New formula for 3-manifold invariants using combinatorial methods.
problem Calculating invariants of 3-manifolds.
method Diagrammatic and combinatorial approach, focusing on the Conway polynomial and Kontsevich integral.
result A general surgery formula for the Casson-Walker-Lescop invariant.
The paper calculates the full asymptotics of analytic torsions for compact orbifolds.
problem Analytic torsions of compact locally symmetric orbifolds.
method Using Selberg's trace formula and geometric localization, the paper evaluates the heat trace and orbital integrals.
result Explicit formula for the asymptotic Ray-Singer analytic torsion of compact orbifolds.
A new formula connects supersymmetric path integrals to Chern-Simons theory.
problem Constructing a rigorous path integral for supersymmetric theories on spin manifolds.
method Using Chen differential forms and non-commutative geometry, a Chern-Simons transgression formula is derived.
result The supersymmetric path integral induces a differential topological invariant.
A general method for analytic inversion in integral geometry is proposed. All classical and some new reconstruction formulas of Radon-John type are obtained by this method. No harmonic analysis and PDE is used.
The paper establishes a Poisson integral formula for bounded pluriharmonic functions on Teichmüller space.
problem Analyzing bounded pluriharmonic functions on Teichmüller space.
method Establishing a Poisson integral formula.
result A Poisson integral formula for bounded pluriharmonic functions on Teichmüller space.
Sharp criterion for Chern-Gauss-Bonnet integral using Q curvature.
problem Quantifying the Chern-Gauss-Bonnet integral using Q curvature.
method New approach involving singular integral estimation.
result Derivation of asymptotic formula for Q curvature equation.
Symplectic groupoids create Poisson integrators for complex systems.
problem Creating efficient integrators for non-linear Poisson structures.
method Recursive solutions of Hamilton-Jacobi equation, interpreted as Lagrangian bisections.
result Constructs Poisson integrators using symplectic groupoids.
In this paper we prove a monotonicity formula for the integral of the mean curvature for complete and proper hypersurfaces of the hyperbolic space and, as consequences, we obtain a lower bound for the integral of the mean curvature and that the integral of the mean curvature is infinity.
In this paper, we prove the integration by parts formula for the non-pluripolar product on a compact Kähler manifold. Our result generalizes the special case of potentials with small unbounded loci proved in [BEGZ10].
The famous Whitney formula relates the winding number of the smooth generic curve in the real plane to the number of its self-intersection points counted with appropriate signs. We extend this formula to smooth immersions of R^n to R^{2n}. Then use this result together with the general technique of Laplace integrals to…
We establish an integral formula on a smooth, precompact domain in a Kahler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula we prove an isoperimetric inequality in terms of a positive lower bound for the Hermitian curvature of the boundary. Combining with a Minkowski t…
Revisits the Gauss-Bonnet formula using double forms.
problem Relating the Euler characteristic to curvature integrals and boundary terms.
method Uses double forms and explores geometric nature of the boundary term.
result Provides new insights into the geometric nature of the Gauss-Bonnet formula.
Given a positive function F on Sn which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in Rn+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in Rn+1. We give some new characteriz…
We prove an analogue of Weyl's Integration Formula for compact Lie groups in the context of polar actions. We also show how certain classical examples from the literature can be viewed as special cases of our result.
The paper explores inequalities on weighted Riemannian manifolds with boundary.
problem Developing inequalities on weighted Riemannian manifolds with boundary.
method Using a Reilly type integral formula associated with the φ-Laplacian.
result Provided inequalities of Brascamp-Lieb type and Colesanti type.
In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2. This localization formula is very well known, but the author hopes to adapt this proof to obtain a more general result in the future.
Kricker defined an invariant of knots in homology 3-spheres which is a rational lift of the Kontsevich integral, and proved with Garoufalidis that this invariant satisfies splitting formulas with respect to a surgery move called null-move. We define a functorial extension of the Kricker invariant and prove splitting fo…
Paper proposes efficient method to calculate Fisher-Bingham distribution normalizing constant.
problem Efficiently calculating the normalizing constant of Fisher-Bingham distributions.
method Numerical integration with continuous Euler transform to Fourier-type integral representation.
result The method is fast and accurate, applicable to high-dimensional distributions.
In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. The purpose is twofold: to provide an interpretation of these formulas in terms of integrals of densities with respect to the canonical measu…
To every Darboux integrable system there is an associated Lie group which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the …
We study the conditions for a nilpotent Lie group to be foliated into subgroups that have square integrable (relative discrete series) unitary representations, that fit together to form a filtration by normal subgroups. Then we use that filtration to construct a class of "stepwise square integrable" representations on …
The paper derives Pizzetti formulae and inverts the Radon transform on spheres.
problem Inverting the Radon transform on spheres.
method Obtained Pizzetti-type formulae on sphere regions, used delta distributions, and derived inversion formulae.
result Derived Pizzetti formulae and inversion formulae for the Radon transform on spheres.