Bubbling and regularity issues in geometric non-linear analysis
Abstract
Numerous elliptic and parabolic variational problems arising in physics and geometry (Ginzburg-Landau equations, harmonic maps, Yang-Mills fields, Omega-instantons, Yamabe equations, geometric flows in general...) possess a critical dimension in which an invariance group (similitudes, conformal groups) acts. This common feature generates, in all these different situations, the same non-linear effect. One observes a strict splitting in space between an almost linear regime and a dominantly non-linear regime which has two major characteristics : it requires a quantized amount of energy and arises along rectifiable objects of special geometric interest (geodesics, minimal surfaces, J-holomorphic curves, special Lagrangian manifolds, mean-curvature flows...).
Cite
@article{arxiv.math/0304396,
title = {Bubbling and regularity issues in geometric non-linear analysis},
author = {Tristan Rivière},
journal= {arXiv preprint arXiv:math/0304396},
year = {2007}
}