Related papers: Parallel Mean Curvature Surfaces in Symmetric Spac…
We show the existence of constant mean curvature surfaces in the homology classes of closed 3-manifolds.
This is an expository article describing the conformalized mean curvature flow, originally introduced by Kazhdan, Solomon, and Ben-Chen. We are interested in applying mean curvature flow to surface parametrizations. We discuss our own…
We give the classification of constant mean curvature rotational surfaces of elliptic, hyperbolic, and parabolic type in the four-dimensional pseudo-Euclidean space with neutral metric.
In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
We prove an inequality bounding the renormalized area of a complete minimal surface in hyperbolic space in terms of the conformal length of its ideal boundary.
In this paper, we obtain an Ecker-Huisken type result for entire graphs with parallel mean curvature.
We prove a Simons type formula for submanifolds with parallel mean curvature vector field in product spaces of type $M^n(c)\times\mathbb{R}$, where $M^n(c)$ is a space form with constant sectional curvature $c$, and then we use it to…
We classify complete orientable hypersurfaces of constant isotropic curvature in space forms. We show that such a hypersurface has constant mean curvature only if it is an isoparametric hypersurface, and that it is minimal if and only if it…
We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope…
We consider a general theory of all possible quadratic, first-order derivative terms of the non-metricity tensor in the framework of Symmetric Teleparallel Geometry. We apply the Noether Symmetry Approach to classify those models that are…
We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…
A study of the generalized Weierstrass system which can be used to induce mean curvature surfaces in three-dimensional Euclidean space is presented.
In this paper, we study $4$-dimensional complete hypersurfaces with $w$-constant mean curvature in the unit sphere. We give a lower bound of the scalar curvature for $4$-dimensional complete hypersurfaces with $w$-constant mean curvature.…
We classify biharmonic submanifolds with certain geometric properties in Euclidean spheres. For codimension 1, we determine the biharmonic hypersurfaces with at most two distinct principal curvatures and the conformally flat biharmonic…
Defined mathematically as critical points of surface area subject to a volume constraint, constant mean curvatures (CMC) surfaces are idealizations of interfaces occurring between two immiscible fluids. Their behavior elucidates phenomena…
Given any nondegenerate k-dimensional minimal submanifold K of codimension greater than 1, we prove the existence of families of constant mean curvature submanifolds, with mean curvature varying from one member of the family to another,…
In this paper, we study generalized constant ratio surfaces in the Euclidean 4-space. We also obtain a classifications of constant slope surfaces.
We investigate geometric invariants of cuspidal edges on focal surfaces of regular surface. In particular, we shall clarify the sign of the singular curvature at a cuspidal edge on a focal surface using singularities of parallel surface of…
In this paper, we investigate the mean curvature flow of submanifolds of arbitrary codimension in $\mathbb{C}\mathbb{P}^m$. We prove that if the initial submanifold satisfies a pinching condition, then the mean curvature flow converges to a…