Regularity of Harmonic Maps between Singular Spaces
报告专家：朱熹平（中山大学）
报告时间：2024年9月27日（星期五）下午15：00-16：00
报告地点：数学学院西303报告厅
报告摘要：Regularity of geometric elliptic equations is one of main themes in geometric analysis. Gromov-Schoen in 1992 initiated to study the theory of harmonic maps into singular spaces. In 1997, J. Jost and F. H. Lin, independently proved that every harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is interior Hölder continuous. Meanwhile, F. H. Lin proposed an open question: can the interior Hölder continuity be improved to interior Lipschitz continuity? J. Jost also asked a similar problem about interior Lipschitz regularity of harmonic maps between singular spaces.
In the first part of this talk I will present an affirmative answer to Jost-Lin’s question. Very recently, Mondino-Semola and Gigli extended our interior Lipschitz regularity to metric measure spaces with synthetic lower bounds on the Ricci curvature, the RCD spaces.
In the second part of this talk, I will report our recent results on the boundary regularity of harmonic maps from RCD spaces to Alexandrov spaces.
专家简介：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。
邀请人：王宝富
