NOTES ON CONFORMAL PERTURBATION OF HEAT KERNELS

Shiliang Zhao ()
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Shiliang Zhao: Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-6

Abstract: Let (M,g) be a smooth n-dimensional Riemannian manifold for n ≥ 3. Consider the conformal perturbation g̃ = hg where h is a smooth bounded positive function on M. Denote by Δ̃ the Laplace–Beltrami operator of manifold (M,g̃). In this paper, we derive the upper bounds of the heat kernels for (−Δ̃)σ with 0 < σ ≤ 1. Moreover, we also investigate the gradient estimates of the heat kernel for Δ̃.

Keywords: Conformal Perturbation; Heat Kernel Estimates (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X2240196X

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