Results 21 to 30 of about 664 (62)

Matrix Inequality for the Laplace Equation

, 2017
Since Li and Yau obtained the gradient estimate for the heat equation, related estimates have been extensively studied. With additional curvature assumptions, matrix estimates that generalize such estimates have been discovered for various time-dependent
Park, Jiewon
core   +1 more source

Commentary on “Nonunique tangent maps at isolated singularities of harmonic maps” by Brian White

, 2018
Immediately following the commentary below, this previously published article is reprinted in its entirety: Brian White, “Nonunique tangent maps at isolated singularities of harmonic maps”, Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 1, 123–129.
W. Minicozzi
semanticscholar   +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

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

A general approach to equivariant biharmonic maps

, 2012
In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which guarantee ...
Montaldo, Stefano, Ratto, Andrea
core   +1 more source

Harmonic morphisms from homogeneous Hadamard manifolds

, 2010
We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This yields new solutions from an important family of homogeneous Hadamard manifolds.
Gudmundsson, Sigmundur, Nordström, Jonas   +1 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 morphisms from the classical compact semisimple Lie groups

, 2007
In this paper we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian ...
Gudmundsson, Sigmundur, Sakovich, Anna
core   +3 more sources

On the Existence of Jenkins-Strebel Differentials Using Harmonic Maps from Surfaces to Graphs

, 1994
We give a new proof of the existence (\cite{HM}, \cite{Ren}) of a Jenkins-Strebel differential $\Phi$ on a Riemann surface $\SR$ with prescribed heights of cylinders by considering the harmonic map from $\SR$ to the leaf space of the vertical foliation ...
Wolf, Michael
core  

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

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