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pro vyhledávání: '"53c44"'
We give an application of a Huisken monotonicity-type formula for the mean curvature flow in a compact smooth manifold with a Riemannian metric that evolves by a shrinking self-similar solution of the extended Ricci flow. Our investigation builds on
Externí odkaz:
http://arxiv.org/abs/2412.19939
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
Autor:
Li, Dasong, Ma, John Man Shun
In this paper we prove two backward uniqueness theorems for extrinsic geometric flow of possibly non-compact hypersurfaces in general ambient complete Riemannian manifolds. These are applicable to a wide range of extrinsic geometric flow, including t
Externí odkaz:
http://arxiv.org/abs/2410.22904
In this paper, we consider the existence of constant mean curvature hypersurfaces with prescribed gradient image. Let $\Omega$ and $\tilde{\Omega}$ be uniformly convex bounded domains in $\mathbb{R}^n$ with smooth boundary. We show that there exists
Externí odkaz:
http://arxiv.org/abs/2411.00817
Autor:
Qin, Lang, Zhang, Qi S.
In this paper, we remove the assumption on the gradient of the Ricci curvature in Hamilton's matrix Harnack estimate for the heat equation on all closed manifolds, answering a question which has been around since the 1990s. New ingredients include a
Externí odkaz:
http://arxiv.org/abs/2409.10379
Autor:
Abiev, Nurlan
We proved that the normalized Ricci flow does not preserve the positivity of Ricci curvature of Riemannian metrics on every generalized Wallach space with $a_1+a_2+a_3\le 1/2$, in particular on the spaces $\operatorname{SU}(k+l+m)/\operatorname{SU}(k
Externí odkaz:
http://arxiv.org/abs/2409.02570
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order temporal discretizations are proposed based on this new formulation.
Externí odkaz:
http://arxiv.org/abs/2408.13443
Autor:
Tam, Luen-Fai
Motivated by previous study on mean curvature flow and prescribed mean curvature flow on spatially compact space or asymptotically flat spacetime, in this work we will find sufficient conditions for the short time existence of prescribed mean curvatu
Externí odkaz:
http://arxiv.org/abs/2406.04667
Let $\Sigma$ be a closed embedded minimal hypersurface in the unit sphere $\mathbb{S}^{m+1}$ and let $\Lambda=\max\limits_{\Sigma}|A|$ be the norm of its second fundamental form. In this work we prove that the first eigenvalue of the Laplacian of $\S
Externí odkaz:
http://arxiv.org/abs/2405.20545
Autor:
Lopez, Rafael, Munteanu, Marian Ioan
We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds $M^3$. Given a conformal vector field $V\in\mathfrak{X}(M^3)$, a conformal trajectory of $V$ is a regular curve $\gamma$ in $M^3$ satisfying $\nabla_{\gamma'}
Externí odkaz:
http://arxiv.org/abs/2405.15890