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
Bach-flat critical metrics for quadratic curvature functionals
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DOI: 10.1007/s10455-018-9606-4
Abstract: In this paper, we study the critical metrics for quadratic curvature functionals involving the Ricci curvature and scalar curvature in the space of Riemannian metrics with unit volume. For these functionals, Einstein metrics are always… read more here.
Keywords: metrics quadratic; curvature functionals; critical metrics; quadratic curvature ... See more keywords
Isoperimetric inequality and Weitzenböck type formula for critical metrics of the volume
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DOI: 10.1007/s11856-019-1930-2
Abstract: We provide an isoperimetric inequality for critical metrics of the volume functional with nonnegative scalar curvature on compact manifolds with boundary. In addition, we establish a Weitzenb\"ock type formula for critical metrics of the volume… read more here.
Keywords: critical metrics; isoperimetric inequality; metrics volume; type formula ... See more keywords