Results 61 to 70 of about 2,699,199 (290)

Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature

Communications on Pure and Applied Mathematics, EarlyView.
Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli, Marco Pozzetta, Daniele Semola   +2 more
wiley   +1 more source

Intersections of Riemannian submanifolds. Variations on a theme by T.J. Frankel [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 1999
Let M^n be an n-dimensional complete connected Riemannian manifold with positive sectional curvature, and let V^r and W^s be two compact, totally geodesic submanifolds of dimensions r and s. In 1961 T.
T. Q. Binh, L. Ornea, L. Tam
doaj  

Biharmonic maps on V-manifolds

International Journal of Mathematics and Mathematical Sciences, 2001
We generalize biharmonic maps between Riemannian manifolds into the case of the domain being V-manifolds. We obtain the first and second variations of biharmonic maps on V-manifolds.
Yuan-Jen Chiang, Hongan Sun
doaj   +1 more source

A Note on the Characterization of Two-Dimensional Quasi-Einstein Manifolds

Mathematics, 2020
In this article, we aim to introduce new classes of two-dimensional quasi-Einstein pseudo-Riemannian manifolds with constant curvature. We also give a classification of 2D quasi-Einstein manifolds of warped product type working in local coordinates.
Gabriel Bercu
doaj   +1 more source

A Note on Constant Mean Curvature Foliations of Noncompact Riemannian Manifolds

International Journal of Mathematics and Mathematical Sciences, 2022
We aimed to study constant mean curvature foliations of noncompact Riemannian manifolds, satisfying some geometric constraints. As a byproduct, we answer a question by M. P. do Carmo (see Introduction) about the leaves of such foliations.
S. Ilias, B. Nelli, M. Soret
doaj   +1 more source

The Dirichlet problem for curvature equations in Riemannian manifolds [PDF]

Indiana University Mathematics Journal, 2013
We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to extend some of the existence theorems of Caffarelli, Nirenberg and Spruck [4] and Ivochkina, Trundinger and Lin [19]
Flavio Cruz, Jorge H. S. de Lira
openaire   +3 more sources

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

Sharp solvability criteria for Dirichlet problems of mean curvature type in Riemannian manifolds: non-existence results [PDF]

Calculus of Variations and Partial Differential Equations, 2019
It is well known that the Serrin condition is a necessary condition for the solvability of the Dirichlet problem for the prescribed mean curvature equation in bounded domains of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym ...
Yunelsy N Alvarez, R. Sa Earp
semanticscholar   +1 more source

A Curvature Identity on a 4-Dimensional Riemannian Manifold [PDF]

Results in Mathematics, 2011
We give a curvature identity derived from the generalized Gauss-Bonnet formula for 4-dimensional compact oriented Riemannian manifolds. We prove that the curvature identity holds on any 4-dimensional Riemannian manifold which is not necessarily compact. We also provide some applications of the identity.
JeongHyeong Park, Yunhee Euh, Kouei Sekigawa   +2 more
openaire   +3 more sources

Regularity and separation for Grušin‐type p‐Laplace operators

Mathematische Nachrichten, EarlyView.
Abstract We analyze p‐Laplace type operators with degenerate elliptic coefficients. This investigation includes Grušin‐type p‐Laplace operators. We describe a separation phenomenon in elliptic and parabolic p‐Laplace type equations, which provide an illuminating illustration of simple jump discontinuities of the corresponding weak solutions ...
Daniel Hauer, Adam Sikora
wiley   +1 more source