A short proof of backward uniqueness for some geometric evolution equations

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4 Citations (Scopus)

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 (Formula presented.)-curvature flow and other higher-order equations.

Original languageEnglish (US)
JournalInternational Journal of Mathematics
DOIs
StateAccepted/In press - 2016

Fingerprint

Curvature Flow
Evolution Equation
Uniqueness
Logarithmic Convexity
Carleman's Inequality
Higher order equation
Uniqueness of Solutions
Energy
Demonstrate
Class

Keywords

  • backward uniqueness
  • Geometric evolution equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "A short proof of backward uniqueness for some geometric evolution equations",
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 (Formula presented.)-curvature flow and other higher-order equations.",
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