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pro vyhledávání: '"53c21"'
Obstructions to the existence of spacelike solitons depending on the growth of the mean curvature $H$ are proved for Lorentzian products $(M\times \mathbb{R}, \bar g=g_M-dt^2)$ with lowerly bounded curvature. The role of these bounds for both the com
Externí odkaz:
http://arxiv.org/abs/2412.10330
Autor:
Verdiani, Luigi, Ziller, Wolfgang
We study initial value problems for various geometric equations on a cohomogeneity manifold near a singular orbit. We show that when prescribing the Ricci curvature, or finding solutions to the Einstein and soliton equations, there exist solutions ne
Externí odkaz:
http://arxiv.org/abs/2412.06058
We extend the buckling and clamped-plate problems to the context of differential forms on compact Riemannian manifolds with smooth boundary. We characterize their smallest eigenvalues and prove that, in the case of Euclidean domains, their spectra on
Externí odkaz:
http://arxiv.org/abs/2412.05612
In this paper we study the rigidity problem for sub-static systems with possibly non-empty boundary. First, we get local and global splitting theorems by assuming the existence of suitable compact minimal hypersurfaces, complementing recent results i
Externí odkaz:
http://arxiv.org/abs/2412.05238
Autor:
Kaya, Seher, López, Rafael
Spacelike intrinsic rotational surfaces with constant mean curvature in the Lorentz-Minkowski space $\E_1^3$ have been recently investigated by Brander et al., extending the known Smyth's surfaces in Euclidean space. Assuming that the surface is intr
Externí odkaz:
http://arxiv.org/abs/2411.19499
Autor:
López, Rafael
We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in the theory
Externí odkaz:
http://arxiv.org/abs/2411.19494
We study a generalization of the manifold-valued Rudin-Osher-Fatemi (ROF) model, which involves an initial datum $f$ mapping from a curved compact surface with smooth boundary to a complete, connected and smooth $n$-dimensional Riemannian manifold. W
Externí odkaz:
http://arxiv.org/abs/2411.19166
Autor:
Luo, Tianci, Wei, Yong
The horospherical $p$-Christoffel-Minkowski problem was posed by Li and Xu (2022) as a problem prescribing the $k$-th horospherical $p$-surface area measure of $h$-convex domains in hyperbolic space $\mathbb{H}^{n+1}$. It is a natural generalization
Externí odkaz:
http://arxiv.org/abs/2411.17328
We complete the classification of semigraphical translators for mean curvature flow in $\mathbb{R}^3$ that was initiated by Hoffman-Mart\'in-White. Specifically, we show that there is no solution to the translator equation on the upper half-plane wit
Externí odkaz:
http://arxiv.org/abs/2411.16889
Autor:
Yu, Jing, Zhu, Xingyu
We give an alternative probabilistic proof of the sharp Assouad--Nagata dimension bound of a doubling metric space. Some partial rigidity results and application to scalar curvature are also discussed. An important technical tool in our arguments is
Externí odkaz:
http://arxiv.org/abs/2411.16660