https://neckpinch.com/authors/vicente-palmer/New arXiv papers by Vicente Palmer, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1805.10055/arxiv:1805.10055Fri, 25 May 2018 00:00:00 GMTAna Hurtado, Vicente Palmer, César Rosales — Let P be a submanifold properly immersed in a rotationally symmetric manifold having a pole and endowed with a weight e^h. The aim of this paper is twofold. First, by assuming certain control on the h-mean curvature of P, we establish comparisons for the h-capacity of extrinsic balls in P, from which we deduce criteria ensuring the h-parabolicity or h-hyperbolicity of P. Second, we employ functions with geometric meaning to describe submanifolds of bounded h-mean curvature which are confined into some regions of the ambient manifold. As a consequence, we derive half-space and Bernstein-type theorems generalizing previous ones. Our results apply for some relevant h-minimal submanifolds appearing in the singularity theory of the mean curvature flow.Mean curvature flowSingularitiesRotational symmetry & warped productsMinimal & CMC surfaces https://neckpinch.com/papers/1802.09833/arxiv:1802.09833Tue, 27 Feb 2018 00:00:00 GMTVicent Gimeno, Vicente Palmer — We study some potential theoretic properties of homothetic solitons Σⁿ of the MCF and the IMCF. Using the analysis of the extrinsic distance function defined on these submanifolds in ℝ^(n+m), we observe similarities and differences in the geometry of solitons in both flows. In particular, we show that parabolic MCF-solitons Σⁿ with n>2 are self-shrinkers and that parabolic IMCF-solitons of any dimension are self-expanders. We have studied too the geometric behavior of parabolic MCF and IMCF-solitons confined in a ball, the behavior of the Mean Exit Time function for the Brownian motion defined on Σ as well as a classification of properly immersed MCF-self-shrinkers with bounded second fundamental form, following the lines of.Mean curvature flowOther curvature flowsInverse mean curvature flowSelf-shrinkers & translators