Isometric embeddings via heat kernel
Abstract
For any n-dimensional compact Riemannian manifold (M,g), we construct a canonical t-family of isometric embeddings It: M->Rq(t), with t>0 sufficiently small and q(t)>>t-n/2. This is done by intrinsically perturbing the heat kernel embedding introduced in [BBG]. As t->0, asymptotic geometry of the embedded images is discussed.
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