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Sharp modulus of
continuity for parabolic equations on manifolds and lower
bounds for the first eigenvalue
Ben Andrews and Julie Clutterbuck |
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Vol. 6 (2013), No. 5, 1013–1024
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 35K05, 35K55, 35P15
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Milestones
Received: 1 April 2012
Accepted: 21 May 2013
Published: 3 November 2013
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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 |
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