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2018•Asian Journal of MathematicsRequires access

On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows

Songzi Li, Xiang‐Dong Li

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Abstract

In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation $\partial_t u=Lu$ associated with the time dependent Witten Laplacian on complete Riemannian manifolds equipped with a variant of the $(K, m)$-super Perelman Ricci flows and the $K$-super Perelman Ricci flows.

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What this paper is about

In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation $\partial_t u=Lu$ associated with the time dependent Witten Laplacian on complete Riemannian manifolds equipped with a variant of the $(K, m)$-super Perelman Ricci flows and the $K$-super Perelman Ricci flows.

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OpenAlex reports 26 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation $\partial_t u=Lu$ associated with the time dependent Witten Laplacian on complete Riemannian manifolds equipped with a variant of the $(K, m)$-super Perelman Ricci flows and the $K$-super Perelman Ricci flows.

Key concepts: Harnack's inequality, Harnack's principle, Mathematics, Ricci flow, Ricci curvature, Pure mathematics, Ricci-flat manifold, Curvature of Riemannian manifolds

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