Geometric analysis and nonlinear PDE
发文时间：2021-07-07 来源：304am永利集团
Geometric analysis and nonlinear PDE
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时间：7.7
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地点：理科一号楼1114
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9：00-9：45
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陈曦（上海数学中心，复旦大学）
锥流形上波的衍射
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9：50-10：35
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李奇睿（浙江大学）
Variational method for some prescribing curvature problems
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10：35-11：00 茶歇
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11：00-11：45
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席东盟（上海大学）
On the Minkowski Problems and related Brunn-Minkowski inequalities
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11：45-14：30 午餐
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14：30-15：15
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陈世炳（中国科技大学）
Introduction to the optimal partial transport problem
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15：20-16：05
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韩邦先（中国科技大学）
最优传输、测度分解定理及应用
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16：00-16：30 茶歇
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16：30- 17：15
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唐岚（华中师范大学）
Boundary Regularity for generalized solutions to the Dirichlet problem of degenerate Monge-Ampere Equations
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报告信息
(以下按照报告顺序排列)
Title: 锥流形上波的衍射œ
Speaker：陈曦（上海数学中心，复旦大学）
Abstract: 锥流形上的拉普拉斯算子的高能量预解式是拟微分算子和锥点上的傅里叶积分算子之和，后者刻画了波在锥点的衍射现象。
Title：Variational method for some prescribing curvature problems
Speaker：李奇睿（浙江大学）
Abstract: Variational method coupled with flow argument is useful in the study of hypersurfaces with prescribed curvature. Following this idea, we discuss the Euclidean hypersurfaces with prescribed centro-affine curvature and the spherical hypersurfaces with prescribed Gauss curvature.
Title：On the Minkowski Problems and related Brunn-Minkowski inequalities
Speaker：席东盟（上海大学）
Abstract: As stated in the title, we will talk about the Minkowski Problems and related Brunn-Minkowski inequalities. The related works are jointed with Huang Yong , Jin Hailin, Leng Gangsong, Wu Yuchi, Zhang Zhenkun, and Zhao Yiming.
Title: Introduction to the optimal partial transport problem
Speaker：陈世炳（中国科技大学）
Abstract: Abstract: In the classical optimal transport problem the masses of the source and target domains are required to be equal, which is a unfavorable restriction in some applications. In this talk we will discuss the optimal partial transport problem which does not have this restriction and also allows one to transport only a portion of mass. This problem was initially formulated and studied by Caffarelli and McCann, and later investigated by Figalli. Recently, it has beed found some applications in image retrieve, machine learning and so on. The talk is based on joint work with Jiakun Liu and Xu-jia Wang.
Title：最优传输、测度分解定理及应用
Speaker：韩邦先（中国科技大学）
Abstract: 近年来, 基于黎曼流形（以及非光滑度量测度空间）上L1-最优传输理论的测度分解定理在度量几何、几何/泛函不等式的研究中得到了广泛的应用。这个定理也是非光滑度量测度空间曲率维数理论发展中的一个里程碑, 它的证明让我们更加深刻地理解了一般度量空间上的最优传输。在本次报告中, 我将向大家介绍这个理论的背景、最新发展和应用。
Title：Boundary Regularity for generalized solutions to the Dirichlet problem of degenerate Monge-Ampere Equations
Speaker：唐岚（华中师范大学）
Abstract: we establish global C^{1, \alpha} regularity for generalized solutions to the Dirichlet problem of the degenerate Monge-Ampere equations with optimal boundary conditions.
