A short proof of backward uniqueness for some geometric evolution equations

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12 Scopus citations

Abstract

We present a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations which includes the Ricci and cross-curvature flows. The proof, based on a classical argument of Agmon-Nirenberg, uses the logarithmic convexity of a certain energy quantity in the place of Carleman inequalities. We further demonstrate the applicability of the technique to the L2-curvature flow and other higher-order equations.

Original languageEnglish (US)
Article number1650102
JournalInternational Journal of Mathematics
Volume27
Issue number12
DOIs
StatePublished - Nov 1 2016

Keywords

  • Geometric evolution equations
  • backward uniqueness

ASJC Scopus subject areas

  • Mathematics(all)

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