Conformal Perturbation of Heat Kernels with applications

Shiliang Zhao

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arXiv · 2012.08757

Conformal Perturbation of Heat Kernels with applications

Shiliang Zhao

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Abstract

Let $(M, g)$ be a smooth n-dimensional Riemannian manifold for $n\ge 2$. Consider the conformal perturbation $\tilde{g}=h g$ where $h$ is a smooth bounded positive function on $M$. Denote by $\tilde{p}_t(x,y)$ the heat kernel of manifolds $(M, \tilde{g})$. In this paper, we derive the upper bounds and gradient estimates of $\tilde{p}_t(x,y)$.

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Shiliang Zhao. 2020-12-16. Conformal Perturbation of Heat Kernels with applications. https://arxiv.org/abs/2012.08757

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