Related papers: Geometric analysis on manifolds with ends

In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell on the…

Some geometric structures with associated Riemannian metrics have been considered in the book.

This survey presents recent Helly-type geometric theorems published since the appearance of the last comprehensive survey, more than ten years ago. We discuss how such theorems continue to be influential in computational geometry and in…

We study scaling function geometry. We show the existence of the scaling function of a geometrically finite one-dimensional mapping. This scaling function is discontinuous. We prove that the scaling function and the asymmetries at the…

The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and…

We obtain sharp estimates for heat kernels and Green's functions on complete noncompact Riemannian manifolds with Euclidean volume growth and nonnegative Ricci curvature. We will then apply these estimates to obtain sharp Moser-Trudinger…

Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…

Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…

We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping…

We discover a new, non-radial example of a manifold whose heat kernel decreases monotonically along all minimal geodesics. We also classify the flat tori with this monotonicity property. Furthermore, we show that for a generic metric on any…

The eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of the eventual concavity properties of the heat flow for…

We study partitions on three dimensional manifolds which minimize the total geodesic perimeter. We propose a relaxed framework based on a $\Gamma$-convergence result and we show some numerical results. We compare our results to those…

We study the low-energy approximation for calculation of the heat kernel which is determined by the strong slowly varying background fields in strongly curved quasi-homogeneous manifolds. A new covariant algebraic approach, based on taking…

In this paper we construct and study isoperimetric functions at infinity for Hadamard manifolds. These quasi-isometry invariants give a measure of the spread of geodesics in such a manifold.

We show that any closed n-dimensional Riemannian manifold can be embedded by a map constructed from heat kernels at a certain time from a finite number of points. Both this time and this number can be bounded in terms of the dimension, a…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

We consider how a closed Riemannian manifold $M$ and its metric tensor $g$ can be approximately reconstructed from local distance measurements. Moreover, we consider an inverse problem of determining $(M,g)$ from limited knowledge on the…

Some curvature properties of Kahler manifolds of indefinite metrics are studied. Analogues of a Kulkarni's theorem are proved for such manifolds.

This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.

Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…