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pro vyhledávání: '"53c43"'
In this note we discuss Gauss maps for M\"obius surfaces in the $n$-sphere, and their applications in the study of Willmore surfaces. One such ``Gauss map'', naturally associated to a Willmore surface that has a dual Willmore surface, is the Lorentzi
Externí odkaz:
http://arxiv.org/abs/2412.11133
Autor:
Hsu, Jia-Lin, Tsui, Mao-Pei
In this paper, inspired by the work Lee-Wan, we researched the rigidity of contracting maps between closed manifolds with positive curvature. We focused on the relation between curvature pinching and contracting conditions involving arbitrary $k$ sin
Externí odkaz:
http://arxiv.org/abs/2412.10620
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:
Badran, Marco
In a closed, oriented ambient manifold $(M^n,g)$ we consider the problem of finding $\mathbb{S}^1$-valued harmonic maps with prescribed singular set. We show that the boundary of any oriented $(n-1)$-submanifold can be realised as the singular set of
Externí odkaz:
http://arxiv.org/abs/2411.14186
Autor:
Ueno, Ryu
The tension field of the identity map from a statistical manifold to a Riemannian statistical manifold, which shares the same Riemannian metric, is the Tchevychev vector field multiplied by negative one. We derive a new class of statistical manifolds
Externí odkaz:
http://arxiv.org/abs/2411.14156
Autor:
Munn, Thomas Jack, Riedler, Oskar
In this note we study $(\lambda,\mu)$-eigenfamilies on compact Riemannian manifolds when $\lambda = \mu$. We show that any compact manifold admitting a $(\lambda,\lambda)$-eigenfunction is a mapping torus and that any $(\lambda,\lambda)$-eigenfamily
Externí odkaz:
http://arxiv.org/abs/2409.16932
We prove that the universal cover of a normal complex algebraic variety admitting a faithful complex representation of its fundamental group is an analytic Zariski open subset of a holomorphically convex complex space. This is a non-proper version of
Externí odkaz:
http://arxiv.org/abs/2408.16441
We prove that harmonic maps into Euclidean buildings, which are not necessarily locally finite, have singular sets of Hausdorff codimension 2, extending the locally finite regularity result of Gromov and Schoen. As an application, we prove superrigid
Externí odkaz:
http://arxiv.org/abs/2408.02783
In this paper we show for every sufficiently large integer $g$ the existence of a complete family of closed and embedded constant mean curvature (CMC) surfaces deforming the Lawson surfaces $\xi_{1,g}$ parametrized by their conformal type. When speci
Externí odkaz:
http://arxiv.org/abs/2407.07130
Autor:
Galkin, Artem, Mariani, Mauro
We investigate the asymptotic behavior, in the long time limit, of the random homology associated to realizations of stochastic diffusion processes on a compact Riemannian manifold. In particular a rigidity result is established: if the rate is quadr
Externí odkaz:
http://arxiv.org/abs/2406.17683