All Questions

Consider a smooth Nash embedding, $f$, of a Riemannian manifold $Σ$ into Euclidean space $\mathbb R^n$. To what extent is this embedding not unique? It is clear that the set of all such embeddings ...

Context: A solution $(M^n, g(t))$ of the Ricci flow is said to encounter a Type III Singularity if $g(t)$ is defined for all $t \geq 0$ and: $$ \sup _{\mathcal{M}^{n} \times[0, \infty)} \|\...

In "The Ricci Flow: An Introduction", the authors define a $\delta$-necklike point of the Ricci flow as a point $(x, t)$ where $$\|\text{Rm} - R (\theta \otimes \theta)\| \leq \delta \|\text{...

Suppose we have a compact smooth riemannian manifold $(M,g)$ and a $\mathcal{C}^2$ diffeomorphism $f$ of this manifold. I am studying the mapping $$\tilde{f}(x)= \exp_{f(x)}^{-1} \circ f \circ \exp_x \...