Open Access
March 2015 Isometric embeddings via heat kernel
Xiaowei Wang, Ke Zhu
J. Differential Geom. 99(3): 497-538 (March 2015). DOI: 10.4310/jdg/1424880984


For any $n$-dimensional compact Riemannian manifold $M$ with smooth metric $g$, we construct a canonical $t$-family of isometric embeddings $I_t : M \to \mathbb{R}^{q(t)}$, with $t \gt 0$ sufficiently small and $q(t) \gg t^{-\frac{n}{2}}$. This is done by intrinsically perturbing the heat kernel embedding introduced in [BBG]. As $t \to 0_{+}$, asymptotic geometry of the embedded images is discussed.


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Xiaowei Wang. Ke Zhu. "Isometric embeddings via heat kernel." J. Differential Geom. 99 (3) 497 - 538, March 2015.


Published: March 2015
First available in Project Euclid: 25 February 2015

zbMATH: 1318.53057
MathSciNet: MR3316975
Digital Object Identifier: 10.4310/jdg/1424880984

Rights: Copyright © 2015 Lehigh University

Vol.99 • No. 3 • March 2015
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