Iterated logarithms and gradient flows
Representation Theory
2018-02-13 v1 Analysis of PDEs
Differential Geometry
Abstract
We consider applications of the theory of balanced weight filtrations and iterated logarithms, initiated in arXiv:1706.01073, to PDEs. The main result is a complete description of the asymptotics of the Yang--Mills flow on the space of metrics on a holomorphic bundle over a Riemann surface. A key ingredient in the argument is a monotonicity property of the flow which holds in arbitrary dimension. The A-side analog is a modified curve shortening flow for which we provide a heuristic calculation in support of a detailed conjectural picture.
Cite
@article{arxiv.1802.04123,
title = {Iterated logarithms and gradient flows},
author = {Fabian Haiden and Ludmil Katzarkov and Maxim Kontsevich and Pranav Pandit},
journal= {arXiv preprint arXiv:1802.04123},
year = {2018}
}
Comments
29 pages, comments encouraged