Abstract
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.
Citation
Xiaowei Wang. Ke Zhu. "Isometric embeddings via heat kernel." J. Differential Geom. 99 (3) 497 - 538, March 2015. https://doi.org/10.4310/jdg/1424880984
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