中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Shi-Zhong Du ( Shantou University)
题 目：On Bernstein Theorem of Affine Maximal Hypersurface
时 间：2023.04.06（星期四）10:30-11:30
地 点：数学院南楼N913
摘 要：Bernstein problem for affine maximal type hypersurfaces has been a core problem in affine geometry. A conjecture proposed firstly by Chern (Proc. Japan-United States Sem., Tokyo, 1977, 17-30) for entire graph and then reformulated by Calabi (Amer. J. Math., 104, 1982, 91-126) to its fully generality asserts that any Euclidean complete, affine maximal type, locally uniformly convex C^4-hypersurface in R^{N+1} must be an elliptic paraboloid. Soon after, the Chern's conjecture was solved completely by Trudinger-Wang (Invent. Math., 140, 2000, 399-422) for dimension N=2 and \theta=3/4. At the same time, it was conjectured by Trudinger-Wang (see also two survey papers by Trudinger [38,39] for the details) that the Bernstein property of the affine maximal hypersurfaces should hold on lower dimensional spaces and fail to hold for higher dimensional cases. On the past twenty years, much efforts were done toward higher dimensional issues but not really successful yet, even for the case of dimension N=3. In this talk, we will present some known results and new results for the problem.
个人简介：Shi-Zhong Du，Associate Professor of Shantou University. Research interestings focus on Fully nonlinear PDEs and Geometric analysis, undertake two NSFC founds and publicate papers on the journals of Calc. Var. & PDEs., Journal of Differential Equations，Transactions of AMS etc.
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