Energy identity for approximate harmonic maps from surfaces to general targets
نویسندگان
چکیده
منابع مشابه
Harmonic maps from degenerating Riemann surfaces
We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in W 1,2 and C modulo bubbles of sequences of such maps. 2000 Mathematics Subject Classification: 58E20
متن کاملEnergy of Twisted Harmonic Maps of Riemann Surfaces
The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function Eρ on Teichmüller space TS which is a qualitative invariant of the holonomy representation ρ of π1(S). Adapting ideas of Sacks-Uhlenbeck, Schoen-Yau and Tromba, we show that the energy function Eρ is proper for any convex cocompact representation of the fundamental ...
متن کاملEnergy Quantization for Harmonic Maps
In this paper we establish the higher-dimensional energy bubbling results for harmonic maps to spheres. We have shown in particular that the energy density of concentrations has to be the sum of energies of harmonic maps from the standard 2dimensional spheres. The result also applies to the structure of tangent maps of stationary harmonic maps at either a singularity or infinity. 0. Introductio...
متن کاملEnergy identity of approximate biharmonic maps to Riemannian manifolds and its application
We consider in dimension four weakly convergent sequences of approximate biharmonic maps to a Riemannian manifold with bi-tension fields bounded in L for p > 4 3 . We prove an energy identity that accounts for the loss of hessian energies by the sum of hessian energies over finitely many nontrivial biharmonic maps on R. As a corollary, we obtain an energy identity for the heat flow of biharmoni...
متن کاملComplexification, Twistor Theory, and Harmonic Maps from Riemann Surfaces
Penrose's twistor theory and many other ideas of mathematical physics are based on the notion of complexification. This notion is explained and examples of its apphcation in physics and mathematics are described. In particular, the well-known analogy between Yang-Mills fields and harmonic maps of Riemann surfaces becomes rather stronger after complexification. This strengthening is the main poi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2017
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2016.09.018