主 题: Geometry Analysis Seminars——On Lawson-Osserman constructions
报告人: Professor Yongsheng Zhang (Northeast Normal University)
时 间: 2017-11-08 13:30-15:30
地 点: Room 1418, Sciences Building No. 1
Abstract: The 1977’ Acta paper by Lawson-Osserman studied the Dirichlet problem for minimal surfaces of high codimensions. Several astonishing results essentially distinct from the case of codimension 1 were obtained there. In particular, they found Lipschitz but non-C1 solutions to the problems associated to Hopf maps between unit spheres. Recently we made systematic developments and discovered certain interesting new phenomena on the existence, non-uniqueness, non-minimizing and minimizing properties of solutions to related Dirichlet problems. This talk is based on joint works with Xiaowei XU and Ling YANG.
H. B. Lawson, Jr. and R. Osserman: Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system. Acta Math. 139 (1977), 1-17.
W. Y. Ding and Y. Yuan: Resolving the singularities of the minimal Hopf cones. J. Partial Diff. Eqs. 19 (2006), 218-231.
X. W. Xu, L. Yang and Y. S. Zhang: On Lawson-Osserman constructions. arXiv: 1610.08162.