Rigidity for critical metrics of the volume functional
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201700240
Abstract: Geodesic balls in a simply connected space forms $\mathbb{S}^n$, $\mathbb{R}^{n}$ or $\mathbb{H}^{n}$ are distinguished manifolds for comparison in bounded Riemannian geometry. In this paper we show that they have the maximum possible boundary volume among… read more here.
Keywords: volume; volume functional; critical metrics; rigidity critical ... See more keywords
Rigidity of critical circle maps
Sign Up to like & getrecommendations! Published in 2018 at "Duke Mathematical Journal"
DOI: 10.1215/00127094-2018-0017
Abstract: We prove that any two $C^4$ critical circle maps with the same irrational rotation number and the same odd criticality are conjugate to each other by a $C^1$ circle diffeomorphism. The conjugacy is $C^{1+\alpha}$ for… read more here.
Keywords: critical circle; circle maps; circle; rigidity critical ... See more keywords