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 Kleinian groups using orbital functions and heat kernels.
We use the heat flow on the loop space of a closed Riemannian manifold to construct an algebraic chain complex. The chain groups are generated by perturbed closed geodesics. The boundary operator is defined in the spirit of Floer theory by counting, modulo time shift, heat flow trajectories that converge asymptotically…
Heat kernel resurgent structure from Picard-Lefschetz theory
Let be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various -related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the reso…
We study the heat trace for both the drifting Laplacian as well as Schrödinger operators on compact Riemannian manifolds. In the case of a finite regularity potential or weight function, we prove the existence of a partial (six term) asymptotic expansion of the heat trace for small times as well as a suitable remainder…
This is an expository paper designed to introduce undergraduates to the Atiyah-Singer index theorem 50 years after its announcement. It includes motivation, a statement of the theorem, an outline of the easy part of the heat equation proof. It includes counting lattice points and knot concordance as applications.
Heat flow on lens spaces settles into Morse functions with four critical points.
Predicts coherence from quantum heat engine noise using machine learning.
The paper compares heat kernels on manifolds with Robin boundary conditions.
We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…
Study on biharmonic map heat flow with monotonicity formula.
Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.
Understanding the heat usage of customers is crucial for effective district heating operations and management. Unfortunately, existing knowledge about customers and their heat load behaviors is quite scarce. Most previous studies are limited to small-scale analyses that are not representative enough to understand the b…
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We show explicitly that the obtaine…
The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic heat kernels, with appropriate modifications, does yield heat kernels for subell…
The spectral properties of p-forms on the fundamental domains of regular tesselations of the d-dimensional sphere are discussed. The degeneracies for all ranks, p, are organised into a double Poincare series which is explicitly determined. In the particular case of coexact forms of rank (d-1)/2, for odd d, it is shown …
Geometric symbols help compute heat invariants.
The paper studies heat kernel asymptotics and proves Morse inequalities.
Derives gradient estimates for CR heat equation on pseudo-Hermitian manifolds.
New method predicts heat load in thermal grids using latent variables.
The Liouville theorem is proven for V T-harmonic map heat flow.
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…
New heat equation method solves intertwining problems in CR geometry.
Paper studies heat flow for maps on manifolds, avoiding singularities.
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres. Finally, as an application, we compute the diagonal of heat kernels for odd dimensional…
Proves upper bounds for heat kernels evolving on manifolds.
Formulae connect heat kernels on glued manifolds.
This paper describes results characterizing the range of the time-t heat operator on various manifolds, including Euclidean spaces, spheres, and hyperbolic spaces. The guiding principle behind these results is this: The functions in the range of the heat operator should be, roughly, those functions having an analytic c…
Study on biharmonic heat equation on manifolds with curvature constraints.
Derives properties of heat kernel for Rumin complex on Heisenberg groups.
The paper studies heat kernels on weighted Riemannian manifolds with curvature bounds.
In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an estimate on Laplacian form of the heat kernel on complete manifolds with nonnegative R…
Paper studies smoothness of bi-conformal heat flow on 4-manifolds.
Study heat content in sub-Riemannian manifolds, obtaining asymptotic expansion.
Near isospectrality forces full isospectrality for compact quotients of symmetric spaces.
In this paper, we study two kind of L^2 norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of positive solutions to these heat flows.
The paper develops heat kernel comparison theorems and applies them to spectral geometry.
Heat flow fails to preserve concavity in curved spaces.
We develop a new method for the calculation of the heat trace asymptotics of the Laplacian on symmetric spaces that is based on a representation of the heat semigroup in form of an average over the Lie group of isometries and obtain a generating function for the whole sequence of all heat invariants.
Bounds on Hessian of heat equation coupled with Ricci flow.
We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction formulas expressing these new invariants in terms of some integral transforms of the u…
This paper proposes an unsupervised learning method to solve heat equations on chips.
Exponential rate of convergence for harmonic heat flow maps.
Sharp time analyticity proved for heat equation on Ricci solitons.
From the uniformization theorem, we know that every Riemann surface has a simply-connected covering space. Moreover, there are only three simply-connected Riemann surfaces: the sphere, the Euclidean plane, and the hyperbolic plane. In this paper, we collect the known heat kernels, or Green's functions, for these three …
In a 1991 paper by Buttig and Eichhorn, the existence and uniqueness of a differential forms heat kernel on open manifolds of bounded geometry was proven. In that paper, it was shown that the heat kernel obeyed certain properties, one of which was a relationship between the derivative of heat kernel of different degree…
New heat semigroup characterizes Sobolev and BV spaces in Carnot groups.
Heat kernel estimates on manifolds with mixed boundary conditions.