Related papers: Geometric analysis on manifolds with ends
Geometrical form of the one-loop divergences induced by conical singularities of background manifolds is studied. To this aim the heat kernel asymptotic expansion on spaces having the structure $C_{\alpha}\times \Sigma$ near singular…
In this paper we continue the analysis of spectral problems in the setting of complete manifolds with fibred boundary metrics, also referred to as $\phi$-metrics, as initiated in our previous work. We consider the Hodge Laplacian for a…
A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
We review recent results about heat kernel estimates based on Kato conditions on the negative part of the Ricci curvature.
In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation…
We survey recent progress in the study of flows of isometric $G_2$-structures on 7-dimensional manifolds, that is, flows that preserve the metric, while modifying the $G_2$-structure. In particular, heat flows of isometric $G_2$-structures…
In this note we apply heat kernels to derive some localization formula in sympletcic geometry, to study moduli spaces of flat connections on a Riemann surface, to obtain the push-forward measures for certain maps between Lie groups and to…
The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new…
The main results of this article are small time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts…
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…
In this article, we prove a general and rather flexible upper bound for the heat kernel of a weighted heat operator on a closed manifold evolving by an intrinsic geometric flow. The proof is based on logarithmic Sobolev inequalities and…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
Whereas for a substantial part, Finite Geometry during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important…
This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit…
The covariant technique for calculating the heat kernel asymptotic expansion for an elliptic differential second order operator is generalized to manifolds with boundary. The first boundary coefficients of the asymptotic expansion which are…
Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…
This paper presents the geometric aspect of the autoencoder framework, which, despite its importance, has been relatively less recognized. Given a set of high-dimensional data points that approximately lie on some lower-dimensional…
In analogy with the spectral theory of geometrically finite hyperbolic manifolds, we initiate the study of resonances on geometrically finite (q+1)-regular graphs of groups. We prove the meromorphic continuation of the resolvent of the…
We study pointwise and $L^p$ gradient estimates of the heat kernel, on manifolds that may have some amount of negative Ricci curvature, provided it is not too negative (in an integral sense) at infinity. We also prove uniform boundedness…