Results 1 to 10 of about 897 (41)
Biharmonic functions on spheres and hyperbolic spaces [PDF]
, 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 2.
Gudmundsson, Sigmundur
arxiv +3 more sources
Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds [PDF]
, 2014 We study 4-dimensional Riemannian manifolds equipped with a minimal and conformal foliation $\mathcal F$ of codimension 2. We prove that the two adapted almost Hermitian structures $J_1$ and $J_2$ are both cosymplectic if and only if $\mathcal F$ is ...
Gudmundsson, Sigmundur
core +1 more source
A note on balance equations for doubly periodic minimal surfaces [PDF]
, 2016 Most known examples of doubly periodic minimal surfaces in $\mathbb{R}^3$ with parallel ends limit as a foliation of $\mathbb{R}^3$ by horizontal noded planes, with the location of the nodes satisfying a set of balance equations. Conversely, for each set
Connor, Peter
core +2 more sources
Smooth long‐time existence of Harmonic Ricci Flow on surfaces
Journal of the London Mathematical Society, Volume 95, Issue 1, Page 277-304, February 2017., 2017 Abstract We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long‐time existence for the Harmonic Ricci Flow with large coupling constant.
Reto Buzano, Melanie Rupflin
wiley +1 more source
Minimizing energy among homotopic maps
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 30, Page 1599-1611, 2004., 2004 We study an energy minimizing sequence {ui} in a fixed homotopy class of smooth maps from a 3‐manifold. After deriving an approximate monotonicity property for {ui} and a continuous version of the Luckhaus lemma (Simon, 1996) on S2, we show that, passing to a subsequence, {ui} converges strongly in W1,2 topology wherever there is small energy ...
Pengzi Miao
wiley +1 more source
Harmonicity of horizontally conformal maps and spectrum of the Laplacian
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 12, Page 709-715, 2002., 2002 We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if Φ : M → N is a horizontally conformal map such that the tension field is divergence free, then Φ is harmonic. Furthermore, if N is noncompact, then Φ must be constant.
Gabjin Yun
wiley +1 more source
Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds
, 2014 We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not K\" ahler ...
Gudmundsson, Sigmundur
core +1 more source
Conformally Flat Circle Bundles over Surfaces [PDF]
Differential Geometry and its Applications (2015), pp. 103-110, 2009 We classify conformally flat Riemannian $3-$manifolds which possesses a free isometric $S^1-$action.
arxiv +1 more source
Harmonic morphisms from four dimensional Lie groups
, 2014 We consider four dimensional Lie groups with left-invariant Riemannian metrics. For such groups we classify left-invariant conformal foliations with minimal leaves of codimension two.
Gudmundsson, Sigmundur, Svensson, Martin
core +1 more source
Biharmonic and harmonic homomorphisms between Riemannian three dimensional unimodular Lie groups [PDF]
arXiv, 2020 We classify biharmonic and harmonic homomorphisms $f:(G,g_1)\rightarrow(G,g_2)$ where $G$ is a connected and simply connected three-dimensional unimodular Lie group and $g_1$ and $g_2$ are left invariant Riemannian metrics.
arxiv