相关论文: Biconservative ideal hypersurfaces in Euclidean sp…
A well-known result asserts that any isometric immersion with flat normal bundle of a Riemannian manifold with constant sectional curvature into a space form is (at least locally) holonomic. In this note, we show that this conclusion…
We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three…
We study the problem posed by F. Burstall of developing a theory of isothermic Euclidean submanifolds of dimension greater than or equal to three. As a natural extension of the definition in the surface case, we call a Euclidean submanifold…
We study $p$-harmonic maps, $p$-harmonic morphisms, biharmonic maps, and quasiregular mappings into submanifolds of warped product Riemannian manifolds ${I}\times_f S^{m-1}(k)\, $ of an open interval and a complete simply-connecteded…
In this paper, we extend several results established for stable minimal hypersurfaces to $\delta$-stable minimal hypersurfaces. These include the regularity and compactness theorems for immersed $\delta$-stable minimal hypersurfaces in…
This paper introduces a biharmonic interpolatory subdivision framework on Riemannian manifolds. In the Euclidean setting, the six-point Deslauriers-Dubuc stencil is characterised as the unique minimiser of a discrete curvature-variation…
We prove that on a compact Riemannian manifold of dimension $3$ or higher, with positive Ricci curvature, the Allen--Cahn min-max scheme (implemented by the first author and N. Wickramasekera in 2020), with prescribing function taken to be…
Biconservative submanifolds arise as a natural relaxation of the biharmonic condition and play an important role in the submanifold theory. In this paper, we study non-CMC biconservative surfaces with parallel normalized mean curvature…
A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean…
We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group.…
Let $M^{n+1}$ be a closed manifold of dimension $3\le n+1\le 7$ equipped with a generic Riemannian metric $g$. Let $c$ be a positive number. We show that, either there exist infinitely many distinct closed hypersurfaces with constant mean…
A well-known theorem by Ruh and Vilms states that the Laplacian of the Gauss map for a smooth immersion into Euclidean space is given by the covariant derivative of the mean curvature vector field. For hypersurfaces, this implies that the…
For constant mean curvature surfaces of class $C^2$ immersed inside Sasakian sub-Riemannian 3-manifolds we obtain a formula for the second derivative of the area which involves horizontal analytical terms, the Webster scalar curvature of…
The purpose of this paper is to study a complete orientable minimal hypersurface with finite index in an $(n+1)$-dimensional Riemannian manifold $N$. We generalize Theorems 1.5-1.6 (\cite{Seo14}). In 1976, Schoen and Yau proved the…
Suppose M_t is a smooth family of compact connected two dimensional submanifolds of Euclidean space E^3 without boundary varying isometrically in their induced Riemannian metrics. Then we show that the mean curvature integrals over M_t are…
We compute a Simons' type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several rigidity results for biharmonic CMC surfaces, putting in evidence the influence of the…
In this article we prove that all boundary points of a minimal oriented hypersurface in a Riemannian manifold are regular, that is, in a neighborhood of any boundary point, the minimal surface is a $\mathcal{C}^{1, \frac14}$ submanifold…
We provide a parametric construction in terms of minimal surfaces of the Euclidean submanifolds of codimension two and arbitrary dimension that attain equality in an inequality due to De Smet, Dillen, Verstraelen and Vrancken. The latter…
In this article we consider PMC surfaces in complex space forms, and we study the interaction between the notions of PMC, totally real and biconservative. We first consider PMC surfaces in non-flat complex space forms and we prove that they…
Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…