Geodesics in heat: A new approach to computing distance based on heat flow
K Crane, C Weischedel, M Wardetzky - ACM Transactions on Graphics …, 2013 - dl.acm.org
We introduce the heat method for computing the geodesic distance to a specified subset (eg,
point or curve) of a given domain. The heat method is robust, efficient, and simple to …
point or curve) of a given domain. The heat method is robust, efficient, and simple to …
The heat method for distance computation
K Crane, C Weischedel, M Wardetzky - Communications of the ACM, 2017 - dl.acm.org
We introduce the heat method for solving the single-or multiple-source shortest path
problem on both flat and curved domains. A key insight is that distance computation can be …
problem on both flat and curved domains. A key insight is that distance computation can be …
Short-time behavior of the heat kernel and Weyl's law on spaces
In this paper, we prove pointwise convergence of heat kernels for mGH-convergent
sequences of RCD^*(K, N) RCD∗(K, N)-spaces. We obtain as a corollary results on the …
sequences of RCD^*(K, N) RCD∗(K, N)-spaces. We obtain as a corollary results on the …
[HTML][HTML] The magazine archive includes every article published in Communications of the ACM for over the past 50 years.
K Crane, C Weischedel, M Wardetzky - Communications of the ACM, 2017 - cacm.acm.org
We introduce the heat method for solving the single-or multiple-source shortest path
problem on both flat and curved domains. A key insight is that distance computation can be …
problem on both flat and curved domains. A key insight is that distance computation can be …
New perspectives on the d'Alembertian from general relativity. An invitation
M Braun - arXiv preprint arXiv:2501.19071, 2025 - arxiv.org
This survey has multiple objectives. First, we motivate and review a new distributional notion
of the d'Alembertian from mathematical relativity, more precisely, a nonlinear $ p $-version …
of the d'Alembertian from mathematical relativity, more precisely, a nonlinear $ p $-version …
[HTML][HTML] Radial processes on RCD⁎(K, N) spaces
K Kuwada, K Kuwae - Journal de Mathématiques Pures et Appliquées, 2019 - Elsevier
In this paper, we show a stochastic expression for the radial processes of Brownian motions
on RCD⁎(K, N)-spaces. It corresponds to the one on Riemannian manifolds. The expression …
on RCD⁎(K, N)-spaces. It corresponds to the one on Riemannian manifolds. The expression …
On uniqueness of maximal coupling for diffusion processes with a reflection
K Kuwada - Journal of Theoretical Probability, 2007 - Springer
A maximal coupling of two diffusion processes makes two diffusion particles meet as early
as possible. We study the uniqueness of maximal couplings under a sort of 'reflection …
as possible. We study the uniqueness of maximal couplings under a sort of 'reflection …
Characterization of maximal Markovian couplings for diffusion processes
K Kuwada - 2009 - projecteuclid.org
Necessary conditions for the existence of a maximal Markovian coupling of diffusion
processes are studied. A sufficient condition described as a global symmetry of the …
processes are studied. A sufficient condition described as a global symmetry of the …
A topological splitting theorem for weighted Alexandrov spaces
K Kuwae, T Shioya - Tohoku Mathematical Journal, Second Series, 2011 - jstage.jst.go.jp
Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition
for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger …
for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger …
Laplacian comparison for Alexandrov spaces
K Kuwae, T Shioya - arXiv preprint arXiv:0709.0788, 2007 - arxiv.org
We consider an infinitesimal version of the Bishop-Gromov relative volume comparison
condition as generalized notion of Ricci curvature bounded below for Alexandrov spaces …
condition as generalized notion of Ricci curvature bounded below for Alexandrov spaces …