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pro vyhledávání: '"53C20"'
In recent work of Kennard, Khalili Samani, and the last author, they generalize the Half-Maximal Symmetry Rank result of Wilking for torus actions on positively curved manifolds to $\mathbb{Z}_2$-tori with a fixed point. They show that if the rank is
Externí odkaz:
http://arxiv.org/abs/2411.00665
Autor:
Reiser, Philipp, Tripaldi, Francesca
We consider the problem of preserving weighted Riemannian metrics of positive Bakry-\'Emery Ricci curvature along surgery. We establish two theorems of this type: One for connected sums, and one for surgeries along higher-dimensional spheres. In cont
Externí odkaz:
http://arxiv.org/abs/2410.18859
Autor:
Das, Anushree, Maity, Soma
Let $M$ be an open manifold of dimension at least $3$, which admits a complete metric of positive scalar curvature. For a function $v$ with bounded growth of derivative, whether $M$ admits a metric of positive scalar curvature with volume growth of t
Externí odkaz:
http://arxiv.org/abs/2410.04121
Autor:
Park, Jiewon
Based on an assumption on the Hessian of the Green function, we derive some monotonicity formulas on nonparabolic manifolds. This assumption is satisfied on manifolds that meet certain conditions including bounds on the sectional curvature and covari
Externí odkaz:
http://arxiv.org/abs/2410.01429
Autor:
Si, Cuifang, Xu, Shicheng
In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=\lambda g$ for some real number $\lambda$. (2) A compac
Externí odkaz:
http://arxiv.org/abs/2409.15707
Autor:
Ghazawneh, Farida
Kennard, Khalili Samani, and Searle showed that for a $\mathbb{Z}_2$-torus acting on a closed, positively curved Riemannian $n$-manifold, $M^{n}$, with a non-empty fixed point set for $n$ large enough and $r$ approximately half the dimension of $M$,
Externí odkaz:
http://arxiv.org/abs/2409.15392
Autor:
Reiser, Philipp
We give new examples of manifolds that appear as cross sections of tangent cones of non-collapsed Ricci limit spaces. It was shown by Colding-Naber that the homeomorphism types of the tangent cones of a fixed point of such a space do not need to be u
Externí odkaz:
http://arxiv.org/abs/2409.11954
Autor:
Alattar, Mohammad
We obtain the Lipschitz analogues of the results Perelman used from Siebenmann's deformation of homeomorphism theory in his proof of the stability theorem. Consequently, we obtain the Lipschitz analogue of Perelman's gluing theorem. Moreover, we obta
Externí odkaz:
http://arxiv.org/abs/2409.06170
In this paper we prove the following Willmore-type inequality: On an unbounded closed convex set $K\subset\mathbb{R}^{n+1}$ $(n\ge 2)$, for any embedded hypersurface $\Sigma\subset K$ with boundary $\partial\Sigma\subset \partial K$ satisfying certai
Externí odkaz:
http://arxiv.org/abs/2409.03321
Autor:
Hamanaka, Shota
We provide new type of decay estimate for scalar curvatures of steady gradient Ricci solitons. We also give certain upper bound for the diameter of a Riemannian manifold whose $\infty$-Bakry--Emery Ricci tensor is bounded by some positive constant fr
Externí odkaz:
http://arxiv.org/abs/2409.00583