Geometric heat comparison criteria for Riemannian manifolds

Karp, L.; Peyerimhoff, N.

Abstract

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. These results are based on the geometric concepts of "(essential) distance from the complement" and "spherical area function". We also discuss some other geometric results about the heat development and illustrate them by examples.

Citation

Karp, L., & Peyerimhoff, N. (2007). Geometric heat comparison criteria for Riemannian manifolds. Annals of Global Analysis and Geometry, 31, 115-145. https://doi.org/10.1007/s10455-006-9038-4

• Journal Article Type: Article
• Acceptance Date: Jun 9, 2006
• Online Publication Date: Oct 5, 2006
• Publication Date: 2007-04
• Journal: Annals of Global Analysis and Geometry
• Print ISSN: 0232-704X
• Electronic ISSN: 1572-9060
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 31
• Pages: 115-145
• DOI: https://doi.org/10.1007/s10455-006-9038-4
• Public URL: https://durham-repository.worktribe.com/output/1553787
• Related Public URLs: http://www.maths.dur.ac.uk/~dma0np/preprints/hotspots.ps