For any surface bounded by a sphere is there always an upper bound of the set of all lengths of all shortest length geodesics between pairs of points?

score 348 · Answer 15 · 2026-03-28 23:58:34

348

Views

$\omega=-ydx+xdy $ is a left-invariant $1$-form on $S^1$

Published on 28 Mar 2026 - 23:58

List Question

Does $\pi^{-1}(A)$ have measure zero?

Non-degeneracy of the cup product in the middle degree

Does Proposition 5.18 also hold if $N$ is changed to a smooth manifold with boundary?

Isomorphism in all homology and cohomology groups

Splitting induces isomorphisms

The Similarity Matrix of graph Laplacian Matrix has different names. What's the difference between these names?

Generalizing the eigenvalues of the Laplacian on $\Omega$ an interval to $\Omega$ an arc on a circle?

How to prove that the two topologies on an embedded submanifold are actually the same one?

PL manifold (piecewise-linear) that is not DIFF nor triangulable: uniquely triangulated or not?

Is the inclusion $i : A \to M$ smooth even if $A$ is not a submanifold?

Manifolds: TOP $\supseteq$ TRI $\supseteq$ PL $\supseteq$ DIFF?

A $2$-dim manifold $M$ is contained in a sphere around the origin if and only if every $\gamma :[0,1] \to M$ satisfies $\int_\gamma xdx+ydy+zdz = 0$

Kerr metric in SageMath causal visualization

For any surface bounded by a sphere is there always an upper bound of the set of all lengths of all shortest length geodesics between pairs of points?

$\omega=-ydx+xdy $ is a left-invariant $1$-form on $S^1$

Trending Questions

Popular # Hahtags

Popular Questions