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arXiv · 2005.09407

On a new type of Inequality related to the Uniform Sublevel Set Problem

John Green
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Abstract

Recently, Steinerberger proved a uniform inequality for the Laplacian serving as a counterpoint to the standard uniform sublevel set inequality which is known to fail for the Laplacian. In this note, we give an elementary proof of this result which highlights a step allowing for adaptations to other situations, for instance, we show that the inequality also holds for the heat operator. We formulate some naturally arising questions.

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John Green. 2020-05-19. On a new type of Inequality related to the Uniform Sublevel Set Problem. https://arxiv.org/abs/2005.09407

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