Conservation laws for conformal invariant variational problems
偏微分方程分析
2007-05-23 v1 微分几何
摘要
We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for harmonic maps into homogeneous spaces. From this form we can recover, without the use of moving frame, all the classical regularity results known for 2-dimensional conformally invariant non-linear elliptic PDE . It enable us also to establish new results. In particular we solve a conjecture by E.Heinz asserting that the solutions to the precribed bounded mean curvature equation in arbitrary manifolds are continuous.
引用
@article{arxiv.math/0603380,
title = {Conservation laws for conformal invariant variational problems},
author = {Riviere Tristan},
journal= {arXiv preprint arXiv:math/0603380},
year = {2007}
}
备注
19 pages