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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

4 votes
3 answers
884 views

Lower bound for the normal injectivity radius

Let $(M,g)$ be a closed Riemannian manifold and let $N$ be a closed embedded submanifold. A tube $T(N,r)$ of radius $r$ of $N$ is defined as the set of points of $M$ which can be reached by a geodesi …
3 votes
1 answer
226 views

Does the R-sphere condition imply that a surface is locally a graph of function on a ball of...

Let $S$ be a $C^2$-regular hypersurface with $S=\partial V$ for some open set $V \subset R^{N+1}$, and let $\nu(P)$ be the exterior unit normal of $S$ with respect to $V$. Assume that $S$ satisfies …