Zobrazeno 1 - 10
of 14 170
pro vyhledávání: '"Manifolds with boundary"'
Autor:
Medvedev, Vladimir
Static manifolds with boundary were recently introduced to mathematics. This kind of manifolds appears naturally in the prescribed scalar curvature problem on manifolds with boundary, when the mean curvature of the boundary is also prescribed. They a
Externí odkaz:
http://arxiv.org/abs/2410.15347
Autor:
Wu, Tong1,2 (AUTHOR) wut977@nenu.edu.cn, Wang, Yong3 (AUTHOR) wangy581@nenu.edu.cn
Publikováno v:
Mathematics (2227-7390). Nov2024, Vol. 12 Issue 22, p3530. 23p.
We prove a scalar-mean rigidity theorem for compact Riemannian manifolds with boundary in dimension less than five by extending Schoen-Yau dimension reduction argument. As a corollary, we prove the sharp spherical radius rigidity theorem and best NNS
Externí odkaz:
http://arxiv.org/abs/2409.14503
We prove Weyl laws for Schr\"odinger operators with critically singular potentials on compact manifolds with boundary. We also improve the Weyl remainder estimates under the condition that the set of all periodic geodesic billiards has measure 0. The
Externí odkaz:
http://arxiv.org/abs/2409.05252
Autor:
Battaglia, Luca, Pu, Yixing
In this paper, we investigate a boundary case of the classical prescribed curvature problem. We focus on prescribing the scalar curvature function K and the boundary mean curvature H on the standard ball. Our analysis extendes previous studies by con
Externí odkaz:
http://arxiv.org/abs/2407.18776
We generalize some fundamental results for noncompact Riemannian manfolds without boundary, that only require completeness and no curvature assumptions, to manifolds with boundary: let $M$ be a smooth Riemannian manifold with boundary $\partial M$ an
Externí odkaz:
http://arxiv.org/abs/2406.11120
Autor:
Yamaguchi, Takao, Zhang, Zhilang
In this paper, we develop the geometry of the limit spaces of compact Riemannian manifolds with boundary, where we assume lower bounds on the sectional curvatures of manifolds and boundaries and the second fundamental forms of boundaries and an upper
Externí odkaz:
http://arxiv.org/abs/2406.00970
Autor:
An, Zhongshan, Huang, Lan-Hsuan
We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderson's conjecture in a strong sense, showing that the map from Einstein m
Externí odkaz:
http://arxiv.org/abs/2405.17577
Autor:
Chen, Xuezhang, Wei, Wei
We establish the global $C^2$-estimates for the modified $\sigma_2$ curvature equation with prescribed boundary mean curvature, and particularly, the local boundary $C^2$ estimates on three-manifolds.
Comment: Comments welcome
Comment: Comments welcome
Externí odkaz:
http://arxiv.org/abs/2405.13134