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11 papers · 2 filters
Halfspace type Theorems for Self-Shrinkers
Marcos P. Cavalcante, Jose M. Espinar
In this short paper we extend the classical Hoffman-Meeks Halfspace Theorem to self-shrinkers, that is: "Let be a hyperplane passing through the origin. The only properly imme…
Canonical extension of submanifolds and foliations in noncompact symmetric spaces
Miguel Dominguez-Vazquez
We propose a method to extend submanifolds, singular Riemannian foliations and isometric actions from a boundary component of a noncompact symmetric space to the whole space. This…
Vector bundles over Lie groupoids and algebroids
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucid…
The Willmore conjecture
Fernando C. Marques, André Neves
The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all. This problem has inspired a lot of mathematics over the years, helping bringing togethe…
Existence of HKT metrics on hypercomplex manifolds of real dimension 8
Gueo Grantcharov, Mehdi Lejmi, Misha Verbitsky
A hypercomplex manifold is a manifold equipped with three complex structures satisfying quaternionic relations. Such a manifold admits a canonical torsion-free connection prese…
Submanifolds With Homothetic Gauss Map In Codimension Two
Guilherme Machado de Freitas
In this article we derive a complete classification of all submanifolds in space forms with codimension two for which the Gauss map is homothetic.