Conformal Embeddings via Heat Kernel

2022/02/06 by Su, Zhitong
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.02665

Abstract

For any n-dimensional compact Riemannian Manifold M with smooth metric g, by employing the heat kernel embedding introduced by Bérard-Besson-Gallot'94, we intrinsically construct a canonical family of conformal embeddings C_t,k: M→ℝ^q(t), with t>0 sufficiently small, q(t)≫ t^-(n)/(2), and k as a function of O(t^l) in proper sense. Our approach involves finding all these canonical conformal embeddings, which shows the distinctions from the isometric embeddings introduced by Wang-Zhu'15.

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