15 citations · 45 across the 17 of their papers we have counts for
8 papers · 1 filter
Small time asymptotics of the entropy of the heat kernel on a Riemannian manifold
Vlado Menkovski, Jacobus W. Portegies, Mahefa Ratsisetraina Ravelonanosy
We give an asymptotic expansion of the relative entropy between the heat kernel of a compact Riemannian manifold and the normalized Riemannian volume for small val…
Semicontinuity of capacity under pointed intrinsic flat convergence
Jeffrey L. Jauregui, Raquel Perales, Jacobus W. Portegies
The concept of the capacity of a compact set in generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multip…
On the regular representation of measures
Jürgen Jost, Rostislav Matveev, Jacobus W. Portegies +1
We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class . The conditio…
Intrinsic flat and Gromov-Hausdorff convergence of manifolds with Ricci curvature bounded below
Rostislav Matveev, Jacobus W. Portegies
We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature uniformly bounded from below and diameter uniformly bounded above…
Semicontinuity of eigenvalues under intrinsic flat convergence
Jacobus W. Portegies
We use the theory of rectifiable metric spaces to define a Dirichlet energy of Lipschitz functions defined on the support of integral currents. This energy is obtained by integrati…
Embeddings of Riemannian manifolds with heat kernels and eigenfunctions
Jacobus W. Portegies
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 an…
Properties of the Intrinsic Flat Distance
J. Portegies, C. Sormani
Here we explore a variety of properties of intrinsic flat convergence. We introduce the sliced filling volume and interval sliced filling volume and explore the relationship betwee…
Semicontinuity of Eigenvalues under Flat Convergence in Euclidean Space
Jacobus W Portegies
Recall that Federer-Fleming defined the notion of flat convergence of submanifolds of Euclidean space to solve the Plateau problem. Here we prove the upper semicontinuity of Neuman…