H�lder continuity of harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature

Bent Fuglede
April 2003
Calculus of Variations & Partial Differential Equations;Apr2003, Vol. 16 Issue 4, p375
Academic Journal
Abstract. This is an addendum to the recent Cambridge Tract "Harmonic maps between Riemannian polyhedra", by J. Eells and the present author. H�lder continuity of locally energy minimizing maps RMULA> from an admissible Riemannian polyhedron X to a complete geodesic space Y is established here in two cases: (1) Y is simply connected and has curvature $\leq 0$ (in the sense of A.D. Alexandrov), or (2) Y is locally compact and has curvature $\leq1$, say, and $\phi(X)$ is contained in a convex ball in Y satisfying bi-point uniqueness and of radius $R<\pi/2$ (best possible). With Y a Riemannian polyhedron, and $R<\pi/4$ in case (2), this was established in the book mentioned above, though with H�lder continuity taken in a weaker, pointwise sense. For X a Riemannian manifold the stated results are due to N.J. Korevaar and R.M. Schoen, resp. T. Serbinowski.


Related Articles

  • Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above. Fuglede, Bent // Calculus of Variations & Partial Differential Equations;Jan2008, Vol. 31 Issue 1, p99 

    The hypothesis of local compactness of the target is removed from an earlier result about interior Hölder continuity of locally energy minimizing maps ϕ from a Riemannian polyhedron ( X, g) to a suitable ball B of radius R < π/2 (best possible) in a geodesic space with curvature...

  • On the concentration-compactness phenomenon for the first Schrodinger eigenvalue. Kokarev, Gerasim // Calculus of Variations & Partial Differential Equations;May2010, Vol. 38 Issue 1/2, p29 

    We study a variational problem for the first eigenvalue ?1(V) of the Schrodinger operator (-?g + V) on closed Riemannian surfaces. More precisely, we explore concentration- compactness properties of sequences formed by ?1-extremal potentials.

  • On Vanishing Theorems for Vector Bundle Valued p-Forms and their Applications. Dong, Yuxin; Wei, Shihshu // Communications in Mathematical Physics;May2011, Vol. 304 Issue 2, p329 

    Let F : [0, ∞) → [0, ∞) be a strictly increasing C function with F(0) = 0. We unify the concepts of F-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce F-Yang-Mills fields, F-degree, F-lower degree, and generalized...

  • Transversally Harmonic Maps between Manifolds with Riemannian Foliations. KONDERAK, JERZY J.; WOLAK, ROBERT A. // Quarterly Journal of Mathematics;Sep2003, Vol. 54 Issue 3, p335 

    We consider leaf preserving maps between manifolds equipped with Riemannian foliations. We construct a transversal tension field for such maps. Then we introduce the notion of transversally harmonic maps. In the last section of the paper we present some examples of transversally harmonic maps.

  • A structure theorem of Dirac-harmonic maps between spheres. Ling Yang // Calculus of Variations & Partial Differential Equations;Aug2009, Vol. 35 Issue 4, p409 

    For an arbitrary Dirac-harmonic map ( f,?) between compact oriented Riemannian surfaces, we shall study the zeros of | ?|. With the aid of Bochner-type formulas, we explore the relationship between the order of the zeros of | ?| and the genus of M and N. On the basis, we could clarify all of...

  • Finsler Spinoptics. Duval, C. // Communications in Mathematical Physics;Oct2008, Vol. 283 Issue 3, p701 

    The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan...

  • Lower Bound for Energies of Harmonic Tangent Unit-Vector Fields on Convex Polyhedra. Majumdar, A.; Robbins, J. M.; Zyskin, M. // Letters in Mathematical Physics;Nov2004, Vol. 70 Issue 2, p169 

    We derive a lower bound for energies of harmonic maps of convex polyhedra into the unit sphere S2 with tangent boundary conditions on the faces. We also establish that C8 maps satisfying tangent boundary conditions are dense with respect to the Sobolev norm in the space of continuous tangent...

  • Book Reviews. Lemaire, Luc // Bulletin of the London Mathematical Society;Oct2002, Vol. 34 Issue 5, p630 

    No abstract available.

  • Integrable Systems in Three-Dimensional Riemannian Geometry. Beffa, G. Mar�; Sanders, J.A.; Jing Ping Wang // Journal of Nonlinear Science;2002, Vol. 12 Issue 2, p143 

    In this paper we introduce a new infinite-dimensional pencil of Hamiltonian structures. These Poisson tensors appear naturally as the ones governing the evolution of the curvatures of certain flows of curves in 3-dimensional Riemannian manifolds with constant curvature. The curves themselves are...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics