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Are a map with constant singular values and its inverse always conjugate through isometries?
Let $U \subseteq \mathbb R^2$ be open, connected and bounded, and let $0<\sigma_1<\sigma_2$ satisfy $\sigma_1 \sigma_2=1$.
Suppose that $f:U \to U$ is a diffeomorphism whose singular values (of $...
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The rigidity of $2$-dim sphere with constant sectional curvature in $\mathbb{R}^n$ for $n> 3$
If there is a smooth isometric embedding $f: (S^2, g)\rightarrow \mathbb{R}^n$, where $(S^2, g)$ is a sphere with Riemannian metric such that the corresponding sectional curvature is equal to $1$, and ...
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