Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Primary: 53C24"'
Autor:
Minemyer, Barry
We prove that there exist K\"{a}hler manifolds that are not homotopy equivalent to a quotient of complex hyperbolic space but which admit a Riemannian metric with nonpositive curvature operator. This shows that K\"{a}hler manifolds do not satisfy the
Externí odkaz:
http://arxiv.org/abs/2401.17101
We prove that entire solutions of the minimal hypersurface equation \[ \mathrm{div}\left(\frac{Du}{\sqrt{1+|Du|^2}}\right) = 0 \] on a complete manifold with $\mathrm{Ric} \ge 0$, whose negative part grows like $\mathcal{O}(r/\log r)$ ($r$ the distan
Externí odkaz:
http://arxiv.org/abs/2310.15620
We show that for any closed nonpositively curved Riemannian 4-manifold $M$ with vanishing Euler characteristic, the Ricci curvature must degenerate somewhere. Moreover, for each point $p\in M$, either the Ricci tensor degenerates or else there is a f
Externí odkaz:
http://arxiv.org/abs/2309.15766
Publikováno v:
Int. Math. Res. Not. IMRN 2024.9 (2024), pp. 7870-7890
We prove a positive mass theorem for spin initial data sets $(M,g,k)$ that contain an asymptotically flat end and a shield of dominant energy (a subset of $M$ on which the dominant energy scalar $\mu-|J|$ has a positive lower bound). In a similar vei
Externí odkaz:
http://arxiv.org/abs/2307.05277
We provide a rigidity statement for the equality case for the Heintze-Karcher inequality in substatic manifolds. We apply such result in the warped product setting to fully remove assumption (H4) in the celebrated Brendle's characterization of consta
Externí odkaz:
http://arxiv.org/abs/2307.04253
Autor:
Placini, Giovanni
We study K\"ahler manifolds that are (weak) relatives, that is, K\"ahler manifolds which share a (locally isometric) submanifold. In particular, we prove that if two K\"ahler manifolds are weak relatives and one of them is projective, then they are r
Externí odkaz:
http://arxiv.org/abs/2306.16174
Autor:
Chernov, Vladimir, Sadykov, Rustam
We formulate conjectures generalizing some known results to the category of virtual Legendrian knots. This includes statements relating virtual Legendrian knots to ordinary Legendrian knots, non-existence of positive virtual Legendrian self isotopy f
Externí odkaz:
http://arxiv.org/abs/2302.03607
Publikováno v:
J. Topol. 16.3 (2023), 855-876
Let $M$ be an orientable connected $n$-dimensional manifold with $n\in\{6,7\}$ and let $Y\subset M$ be a two-sided closed connected incompressible hypersurface which does not admit a metric of positive scalar curvature (abbreviated by psc). Moreover,
Externí odkaz:
http://arxiv.org/abs/2205.12174
Autor:
Alexandrov, Victor
Publikováno v:
J. Geom. 112, No. 3, Paper No. 41, 7 p. (2021)
We prove that first-order flexes of smooth surfaces in Euclidean 3-space, which are tangent to the set of all nonrigid surfaces, can be extended to second-order flexes.
Comment: 4 pages, 1 figure
Comment: 4 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2109.03503
Autor:
Hu, Zejun, Xing, Cheng
In this paper, based on the classical K. Yano's formula, we first establish an optimal integral inequality for compact Lagrangian submanifolds in the complex space forms, which involves the Ricci curvature in the direction $J\vec{H}$ and the norm of
Externí odkaz:
http://arxiv.org/abs/2102.01308