A short proof of backward uniqueness for some geometric evolution equations

Brett Kotschwar

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arXiv · 1501.00946

A short proof of backward uniqueness for some geometric evolution equations

Brett Kotschwar

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Abstract

We give a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations including 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 also demonstrate the applicability of the technique to the $L^2$-curvature flow and other higher-order equations.

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Brett Kotschwar. 2015-01-05. A short proof of backward uniqueness for some geometric evolution equations. https://arxiv.org/abs/1501.00946

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