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@arXiv_mathDG_bot@mastoxiv.page
2025-06-03 07:36:44

Stability and rigidity results of space-like hypersurface in the Minkowski space
Jianhua Chen, Haiyun Deng, Haiqin Xie, Jiabin Yin
arxiv.org/abs/2506.01012

Stability and rigidity results of space-like hypersurface in the Minkowski space
In this paper, we establish some rigidity theorems for space-like hypersurfaces in Minkowski space by using a Weinberger-type approach with P-functions and integral identities. Firstly, for space-like hypersurfaces $M$ represented as graphs $x_{n+1}=u(x)$ over domain $Ω\subset\mathbb R^n$, if higher-order mean curvature ratio $\frac{H_{k}}{H_l}(l

@arXiv_mathAG_bot@mastoxiv.page
2025-06-04 13:44:01

This arxiv.org/abs/2411.01953 has been replaced.
initial toot: mastoxiv.page/@arXiv_mat…

Twists of intermediate Jacobian fibrations
We study the sections, Tate--Shafarevich twists, and the period for an OG10 hyperkähler Lagrangian associated to a cubic fourfold. To do so, we introduce the analytic relative Jacobian sheaf for a Lagrangian fibration of a hyperkähler variety. The Tate--Shafarevich group parameterizing twists is isomorphic to the first cohomology group of this sheaf and we compute it in terms of certain analytic Brauer groups associated to the cubic fourfold. We prove that the primitive Hodge lattice of the c…

@bogo@hapyyr.com
2025-05-27 06:01:38

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@arXiv_mathDG_bot@mastoxiv.page
2025-05-29 10:19:54

This arxiv.org/abs/2412.17410 has been replaced.
initial toot: mastoxiv.page/@arXiv_mat…

Rigidity of spacelike hypersurface with constant curvature and intersection angle condition
In the Minkowski space, we consider a spacelike hypersurface with boundary, which can be written as a graph on a spacelike hyperplane. We prove that, if its $k$-th mean curvature is constant, and its boundary is on the hyperplane with constant intersection angles, then the hypersurface must be a part of a hyperboloid, unless it is entirely contained in the hyperplane. This result can be seen as an analog of the sphere theorem for the hypersurface of constant $k$-th mean curvature in the Euclide…