Vol. 6, No. 5, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue

Ben Andrews and Julie Clutterbuck

Vol. 6 (2013), No. 5, 1013–1024
Abstract

We derive sharp estimates on the modulus of continuity for solutions of the heat equation on a compact Riemannian manifold with a Ricci curvature bound, in terms of initial oscillation and elapsed time. As an application, we give an easy proof of the optimal lower bound on the first eigenvalue of the Laplacian on such a manifold as a function of diameter.

Keywords
eigenvalue lower bound, heat equation, modulus of continuity
Mathematical Subject Classification 2010
Primary: 35K05, 35K55, 35P15
Milestones
Received: 1 April 2012
Accepted: 21 May 2013
Published: 3 November 2013
Authors
Ben Andrews
Mathematical Sciences Institute
Australian National University
Building 27
Canberra ACT 0200
Australia
Mathematical Sciences Center
Tsinghua University
Julie Clutterbuck
Mathematical Sciences Institute
Australian National University
Canberra ACT 0200
Australia