# Subelliptic harmonic maps from Carnot groups

## Related Articles

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In this paper, the author considers a class of complete noncompact Riemannian manifolds which satisfy certain conditions on Ricci curvature and volume comparison. It is shown that any harmonic map with finite energy from such a manifold M into a normal geodesic ball in another manifold N must be...

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Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.

- Heat Flow of Harmonic Maps Whose Gradients Belong to $$L^{n}_{x}L^{\infty}_{t}$$. Changyou Wang; Sverak, V. // Archive for Rational Mechanics & Analysis;May2008, Vol. 188 Issue 2, p351
For any compact n-dimensional Riemannian manifold ( M, g) without boundary, a compact Riemannian manifold $$N \subset {\mathbb{R}}^{k}$$ without boundary, and 0 < T â‰¦ +âˆž, we prove that for n â‰§ 4, if u : M Ã— (0, T] â†’ N is a weak solution to the heat flow of harmonic...

- Fourth order approximation of harmonic maps from surfaces. Lamm, Tobias // Calculus of Variations & Partial Differential Equations;Oct2006, Vol. 27 Issue 2, p125
Let $$(M^2,g)$$ be a compact Riemannian surface and let $$(N^n,h)$$ be a compact Riemannian manifold, both without boundary, and assume that N is isometrically embedded into some R l . We consider a sequence $$u_\epsilon \in C^\infty (M,N) (\epsilon \to 0$$ of critical points of the functional...

- Harmonic cellular maps which are not diffeomorphisms. Farrell, F.T.; Ontaneda, P. // Inventiones Mathematicae;Dec2004, Vol. 158 Issue 3, p497
Describes the construction of harmonic cellular maps between closed negatively curved Riemannian manifolds which are not diffeomorphisms. Relationship between the Poincare Conjecture in low dimensional topology and the existence of a certain type of harmonic map; Eells-Sampson theorem; Use of...

- On the regularity theories for harmonic maps from Finsler manifolds. Zhu, Wei // Chinese Annals of Mathematics;Jul2012, Vol. 33 Issue 4, p595
The author studies the regularity of energy minimizing maps from Finsler manifolds to Riemannian manifolds. It is also shown that the energy minimizing maps are smooth, when the target manifolds have no focal points.

- A LIOUVILLE THEOREM FOR F-HARMONIC MAPS WITH FINITE F-ENERGY. Kassi, M'hamed // Electronic Journal of Differential Equations;2006, Vol. 2006, p1
Let (M, g) be a m-dimensional complete Riemannian manifold with a pole, and (N, h) a Riemannian manifold. Let F : R+ ? R+ be a strictly increasing Cï¿½ function such that F(0) = 0 and dF := sup(tF'0(t)(F(t))-1) < 1. We show that if dF < m/2, then every F-harmonic map u : M ? N with finite...

- Biharmonic maps between doubly warped product manifolds. Perktaş, Selcen Yüksel; Kılıç, Erol // Balkan Journal of Geometry & Its Applications;2010, Vol. 15 Issue 2, p1591
In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds B and F into the nontrivial (proper) doubly warped product manifold fB xb F can not be proper biharmonic maps. Also we analyze the conditions for the...

- Regularity of Dirac-Harmonic Maps. Changyou Wang; Deliang Xu // IMRN: International Mathematics Research Notices;Oct2009, Vol. 2009 Issue 20, p3759
For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle S M, and any compact Riemannian manifold N, we show an e-regularity theorem for weakly Dirac-harmonic maps (f, ?):M ? S M ? N ? f*TN. As a consequence, any weakly Dirac-harmonic map is proven...