Conformal Embeddings via Heat Kernel

For any n-dimensional compact Riemannian Manifold $M$ with smooth metric $g$, by using the heat kernel embedding introduced in [BBG], we construct a canonical family of conformal embeddings $C_{t,k}$: $M\rightarrow\mathbb{R}^{q(t)}$, with $t>0$ sufficiently small, $q(t)\gg t^{-\frac{n}{2}}$, and $k$ as a function of $O(t^l)$ in proper sense. This is done by finding all the conformal embeddings to overcome the differences from the isometric embeddings introduced in [WZ]