An $\varepsilon$-regularity theorem for line bundle mean curvature flow

Autor: Han, Xiaoli, Yamamoto, Hikaru
Rok vydání: 2019
Předmět:
Druh dokumentu: Working Paper
Popis: In this paper, we study the line bundle mean curvature flow defined by Jacob and Yau. The line bundle mean curvature flow is a kind of parabolic flows to obtain deformed Hermitian Yang-Mills metrics on a given K\"ahler manifold. The goal of this paper is to give an $\varepsilon$-regularity theorem for the line bundle mean curvature flow. To establish the theorem, we provide a scale invariant monotone quantity. As a critical point of this quantity, we define self-shrinker solution of the line bundle mean curvature flow. The Liouville type theorem for self-shrinkers is also given. It plays an important role in the proof of the $\varepsilon$-regularity theorem.
Comment: 41 pages. v2: some comments were added in the introduction. v3: some comments were added in the information of funds
Databáze: arXiv