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.
Study uses renormalized area to determine metric expansion from minimal surfaces.
Researchers compute zeta-determinants and analytic torsion for metric mapping tori.
Study uniquely determines Riemannian metric derivatives from boundary data.
On compact surfaces with or without boundary, Osgood, Phillips and Sarnak proved that the maximum of the determinant of the Laplacian within a conformal class of metrics with fixed area occurs at a metric of constant curvature and, for negative Euler characteristic, exhibited a flow from a given metric to a constant cu…
We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalue…
For singular metrics, there is no Quillen metric formalism on cohomology determinant. In this paper, we develop an admissible theory, with which the arithmetic Deligne-Riemann-Roch isometry can be established for singular metrics. As an application, we first study Weil-Petersson metrics and Takhtajan-Zograf metrics on …
We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary for a class of higher-order elliptic boundary value problems.
As is well known, a metric on a manifold determines a unique symmetric connection for which the metric is parallel: the Levi-Civita connection. In this paper we investigate the inverse problem: to what extent is the metric of a Riemannian manifold determined by its Levi-Civita connection? It is shown that for a generic…
It is shown that for any piecewise-linear closed orientable manifold of odd dimension there exists an invariantly defined metric on the determinant line of cohomology with coefficients in an arbitrary flat bundle E over the manifold (E is not required to be unimodular). The construction of this metric (called Poincare …
New proof shows holomorphic sectional curvature fully determines curvature tensor.
We examine homogeneous metrics on spheres and determine which ones have positive sectional curvature. The answer is subtle and surprisingly difficult to prove. In some cases we also determine their pinching constants. This completes the classification of all homogeneous metrics with positive curvature (apart from one s…
Graph Laplace operators uniquely identify metrics and densities on manifolds.
For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange struc…
Paper proves DN map determination for simple surfaces with low regularity metrics.
Researchers solve a formally determined inverse problem in Lorentzian geometry.
In this paper, we introduce the notion of Einstein-reversibility for Finsler met- rics. We study a class of p-power Finsler metrics determined by a Riemann metric and 1-form which are of Einstein-reversibility. It shows that such a class of Finsler metrics of Einstein-reversibility are always Einstein metrics. In parti…
Determining the associated metrics we get a local classification of contact metric three manifolds.
Study on 4-manifolds for special Kähler metrics with constant Ricci determinant.
Stokes equations help uniquely identify manifold metrics from boundary data.
We present and prove Polyakov-Alvarez type comparison formulas for the determinants of Friederichs extensions of Laplacians corresponding to conformally equivalent metrics on a compact Riemann surface with conical singularities. In particular, we find how the determinants depend on the orders of conical singularities. …
Derives formulas for determinant of Laplacian on curved surfaces.
Study discrete analog of zeta-determinant maximization on triangulated surfaces.
When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask: which curves' lengths do we really need to know? It is a result of Duchin--Leininger--Rafi that any flat metric induced by a unit-norm quadratic differential is determined by its marked simple length spectrum. We genera…
Analytic metrics are uniquely determined by their scattering map.
The paper calculates the Saito determinant for Coxeter discriminant strata.
Anisotropic metric on manifolds uniquely determined by boundary data.
We investigate the rigidity of hyperbolic cone metrics on -manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to i…
Study on determining metrics via Dirichlet-to-Neumann map for harmonic maps.
We study comparison formulas for -regularized determinants of self-adjoint extensions of the Laplacian on flat conical surfaces of genus . The cases of trivial and non-trivial holonomy of the metric turn out to differ significantly.
There is a one-to-one correspondence between associated families of generic conformally flat (local-)hypersurfaces in 4-dimensional space forms and conformally flat 3-metrics with the Guichard condition. In this paper, we study the space of conformally flat 3-metrics with the Guichard condition: for a conformally flat …
On an open manifold, the spaces of metrics or connections of bounded geometry, respectively, split into an uncountable number of components. We show that for a pair of metrics or connections, belonging to the same component, relative -functions, determinants, torsion for pairs of generalized Dirac operators are well…
Formula derived for spectral determinant of sphere with conical singularities.
Study of symmetries in 3D Lie groups, determining index and moduli space properties.
The paper calculates determinants for Laplacians on spinor bundles over surfaces with flat metrics.
New proofs confirm travel time data determine simple metrics on a disc.
Performance metrics (error measures) are vital components of the evaluation frameworks in various fields. The intention of this study was to overview of a variety of performance metrics and approaches to their classification. The main goal of the study was to develop a typology that will help to improve our knowledge a…
Study reveals how boundary wave operator determines metric properties on anti-de Sitter spacetimes.
The Degasperis-Procesi equation's solutions define pseudospherical metrics and can lead to surface collapse.
We determine all Finsler metrics of Randers type for which the Riemannian part is a scalar multiple of the Euclidean metric, on an open subset of the Euclidean plane, whose geodesics are circles. We show that the Riemannian part must be of constant Gaussian curvature, and that for every such Riemannian metric there is …
Investigates special metrics in hypercomplex geometry.
This paper completes a programme to determine which toric surfaces admit Kahler metrics of constant scalar curvature/
Researchers found all special metrics in 4D for certain curvature functionals.
In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line bundle was identified with the pullback of the determinant line b…
Let Σbe a compact surface of type (g, n), n > 0, obtained by removing n disjoint disks from a closed surface of genus g. Assuming χ(Σ)<0, we show that on Σ, the set of flat metrics which have the same Laplacian spectrum of Dirichlet boundary condition is compact in the C^\infty topology. This isospectral compactness ex…
Study finds conditions for conformal deformations to constant scalar curvature in conic metrics.
In the same way that a contact manifold determines and is determined by a symplectic cone, a Sasaki manifold determines and is determined by a suitable Kahler cone. Kahler-Sasaki geometry is the geometry of these cones. This paper presents a symplectic action-angle coordinates approach to toric Kahler geometry and how …
We derive a precise asymptotic expansion of the complete Kähler-Einstein metric on the punctured Riemann sphere with three or more omitting points. By using Schwarzian derivative, we prove that the coefficients of the expansion are polynomials on the two parameters which are uniquely determined by the omitting points. …
Proves existence of Yamabe metrics on conical manifolds with conical points and links.