Relatively maximum volume rigidity in Alexandrov geometry

Details Relatively maximum volume rigidity in Alexandrov geometry Relatively maximum volume rigidity in Alexandrov geometry

2011-06-23

arxiv.org/abs/1106.4611v4

Mathematics

Differential Geometry

28 pages

Scientific paper

Given a compact Alexadrov $n$-space $Z$ with curvature curv $\ge \kappa$, and let $f: Z\to X$ be a distance non-increasing onto map to another Alexandrov $n$-space with curv $\ge \kappa$. The relative volume rigidity conjecture says that if $X$ achieves the relative maximal volume i.e. $vol(Z)=vol(X)$, then $X$ is isometric to $Z/\sim$, where $z, z'\in\partial Z$ and $z\sim z'$ if only if $f(z)=f(z')$. We will partially verify this conjecture, and give a classification for compact Alexandrov $n$-spaces with relatively maximal volume. We will also give an elementary proof for a pointed version of Bishop-Gromov relative volume comparison with rigidity in Alexandrov geometry.

Affiliated with

Also associated with

No associations

Rating

Relatively maximum volume rigidity in Alexandrov geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Relatively maximum volume rigidity in Alexandrov geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Relatively maximum volume rigidity in Alexandrov geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-469359