Results 21 to 30 of about 632 (68)

Bernstein Theorems for Space-like Graphs with Parallel Mean Curvature and Controlled Growth

, 2007
In this paper, we obtain an Ecker-Huisken type result for entire graphs with parallel mean curvature.Comment: 12 ...
ALias, Calabi, Cao, Cheng, Chern, Ecker, Hildebrandt, Jost, Jost, Marsden, Smoczyk, Treibergs, Wang, Wang, Xin, Xin, Xin, Yuxin Dong   +17 more
core   +2 more sources

III-harmonic Curves in SL2ℝ˜\widetilde {{\rm{S}}{{\rm{L}}_2}\mathbb{R}} Space

Annals of the West University of Timisoara: Mathematics and Computer Science
Some work has been done in the study of non-geodesic III-harmonic curves in some model spaces. In this paper, we study III-harmonic curves in SL2ℝ˜\widetilde {{\rm{S}}{{\rm{L}}_2}\mathbb{R}} space. We give necessary and su cient conditions for helices to
Senoussi Bendehiba
doaj   +1 more source

Biharmonic functions on spheres and hyperbolic spaces

, 2018
We construct new explicit proper r-harmonic functions on the standard n-dimensional sphere S^n and hyperbolic space H^n for any r\ge 1 and n\ge ...
Gudmundsson, Sigmundur
core   +1 more source

Some aspects of the global geometry of entire space-like submanifolds

, 2001
We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global solutions of Monge-Ampere ...
Jost, Juergen, Xin, Yuan-Long
core   +1 more source

Curvature conditions for complex-valued harmonic morphisms

, 2014
We study the curvature of a manifold on which there can be defined a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second ...
Nordström, Jonas
core   +1 more source

A note on Biharmonic functions on the Thurston geometries

, 2017
We construct new explicit proper biharmonic functions on the $3$-dimensional Thurston geometries $\Sol$, $\Nil$, $\SL2$, $H^2\times\rn$ and $S^2\times\rn$
Gudmundsson, Sigmundur
core   +1 more source

Biharmonic Riemannian submersions from 3-manifolds

, 2010
An important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a surface into 3-dimensional Euclidean space is biharmonic if and only if it is harmonic (i.e, minimal). In
B. Fuglede, B. O’Neill, B.Y. Chen, B.Y. Chen, E. Loubeau, G.Y. Jiang, G.Y. Jiang, I. Dimitrić, P. Baird, P. Baird, R. Caddeo, T. Hasanis, T. Ishihara, Y.-L. Ou, Ye-Lin Ou, Ze-Ping Wang   +15 more
core   +1 more source

Partial Regularity for Stationary Solutions to Liouville-Type Equation in dimension 3

, 2008
In dimension $n=3$, we prove that the singular set of any stationary solution to the Liouville equation $-\Delta u=e^u$, which belongs to $W^{1,2}$, has Hausdorff dimension at most 1.Comment: 20 ...
Da Lio, Francesca
core   +2 more sources

Harmonic Maps with Prescribed Singularities on Unbounded Domains

, 1995
The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities $\p\colon\R^3\sm\Sigma\to\H^{k+1}_\C$ into the $(k+1)$-dimensional complex hyperbolic space.
Weinstein, Gilbert
core   +2 more sources

On p-harmonic self-maps of spheres. [PDF]

Calc Var Partial Differ Equ, 2023
Branding V, Siffert A.
europepmc   +1 more source