报告摘要：
In 1964, Eells-Sampson proved the celebrated long-time existence and convergence for the harmonic map heat flow into non-positively curved Riemannian manifolds. In 1992, Gromov and Schoen initiated the study of harmonic maps into CAT(0) metric spaces. In the 1990s, Mayer and Jost independently obtained the weak solutions for the harmonic map heat flow into CAT(0) spaces. The weak solutions enjoy the favorable long-time existence, uniqueness and well-established long-time behaviors. It remained an open question to ask if the weak solutions possess the Lipschitz regularity. Recently, Lin, Segatti, Sire, and Wang obtained a partial answer. They used elliptic approximation method to prove that the weak solutions are Lipschitz in space and 1/2 -Hölder continuous in time, for a wide class of CAT(0) spaces.
In this talk I report my joint work with Hui-Chun Zhang to give a complete answer to the question. We show that every weak solution of the harmonic map heat flow into CAT(0) spaces is Lipschitz continuous in both space and time. We also establish an Eells-Sampson-type Bochner inequality. Very recently, Lin and Wang obtained an alternative proof.
报告人简介：
朱熹平，中山大学教授。1998 年度国家杰出青年科学基金获得者；2001年度国家重大人才工程入选者；2002 和 2013 年度全国百篇优秀博士学位论文指导教师；2015 年度国家自然科学基金创新研究群体项目学术带头人。曾获1991年度中国科学院自然科学奖二等奖； 2004 年度 ICCM 晨兴数学银奖；2013 年度教育部高等学校自然科学奖一等奖； 2016 年度 ICCM 陈省身奖；2016 年度国家自然科学奖二等奖等。朱熹平教授主要从事几何分析领域的研究，在 Ricci 流、度量几何和广义相对论的数学理论等方面取得了若干重要贡献。
