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We consider the Jacobi operator, defined on a closed oriented hypersurfaces immersed in the Euclidean space with the same volume of the unit sphere. We show a local generalization for the classical result of the Willmore functional for the Euclidean
Externí odkaz:
http://arxiv.org/abs/2001.03137
Autor:
Montenegro, J. Fabio
Let $M$ be a Riemannian manifold of dimension $n+1$ with smooth boundary and $p\in \partial M$. We prove that there exists a smooth foliation around $p$ whose leaves are submanifolds of dimension $n$, constant mean curvature and its arrive perpendicu
Externí odkaz:
http://arxiv.org/abs/1904.11867
Autor:
Montenegro, J.1, Morante, J.2, Acosta, M.2, Jaimez, R.3, Carranza, M.2, Bru, R.4, Huebla, V.5, Morante, L.6, Abasolo, F.7, Sepulveda, N.8, Quiñones, J.8 john.quinones@ufrontera.cl
Publikováno v:
JAPS: Journal of Animal & Plant Sciences. Dec2023, Vol. 33 Issue 6, p1314-1321. 8p.
Akademický článek
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In this paper we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplacian contains an interval. The result
Externí odkaz:
http://arxiv.org/abs/1205.5428
We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total s
Externí odkaz:
http://arxiv.org/abs/1009.3467
We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, w
Externí odkaz:
http://arxiv.org/abs/1001.0853
We give sharp sectional curvature estimates for complete immersed cylindrically bounded $m$-submanifolds $\phi:M\to N\times\mathbb{R}^{\ell}$, $n+\ell\leq 2m-1$ provided that either $\phi$ is proper with the second fundamental form with certain contr
Externí odkaz:
http://arxiv.org/abs/0907.5025
J. Nash proved that the geometry of any Riemannian manifold M imposes no restrictions to be embedded isometrically into a (fixed) ball B_{\mathbb{R}^{N}}(1) of the Euclidean space R^N. However, the geometry of M appears, to some extent, imposing rest
Externí odkaz:
http://arxiv.org/abs/0809.2563
Publikováno v:
The Journal of Geometric Analysis, v. 20, p. 63-71, 2010.
We show that the spectrum of a complete submanifold properly immersed into a ball of a Riemannian manifold is discrete, provided the norm of the mean curvature vector is sufficiently small. In particular, the spectrum of a complete minimal surface pr
Externí odkaz:
http://arxiv.org/abs/0809.1173