Chuanqiang Chen (Ningbo University)
Title: Strict power convexity of solutions to elliptic PDEs
Abstract: The convexity of solutions to elliptic PDEs is an important issue. In this talk, we establish some strict power convexity results in dimensions 2 and 3 for fully nonlinear elliptic PDEs by the Constant Rank Theorem method.
This is a joint work with Haohao Jia, Jiawei Xiong and Yan Ma.
Genggeng Huang (Fudan University)
Title: Monge-Ampere equations in convex polytopes
Abstract: In this talk, we will talk about our recent regularity results of Monge-Ampere equations in convex polytopes with Guillemin boundary condition or Dirichlet boundary condition.
This is a joint work with Weiming Shen.
Yalong Shi (Nanjing University)
Title: Green function rigidity problem for GJMS operators and mass of hypersurfaces
Abstract: The Green functions of GJMS operators on spheres have special forms involving only the extrinsic distance. It is conjectured that this property uniquely characterize round spheres among closed hypersurfaces in Euclidean spaces. In this talk, we shall prove this conjecture for conformal Laplacian. The main tools are the Positive Mass Theorem and Hartman-Nirenberg's theorem on complete flat hypersurfaces. Parallel results concerning Paneitz operator will also be discussed.
This is joint work with Xuezhang Chen and Jiaxue Gan.
Chong Song (Xiamen University)
Title: Yang-Mills-Higgs-Schrödinger flow
Abstract: In this talk ,we will introduce the Yang-Mills-Higgs-Schrödinger(YMHS) flow, which is the infinite dimensional Hamiltonian flow of the Yang-Mills-Higgs functional defined on a holomorphic fiber bundle. It originates from the Schrödinger-Chern-Simons system and natually extends the Schrödinger map flow introduced by Ding-Wang to a gauged setting. We will discuss its geometric structures and also local well-posedness.
This is a joint work with Bo Chen.
Zhizhang Wang (Fudan University)
Title: Second boundary value problem for Hessian curvature equations and curvature flows
Abstract: We establish the existence of strictly convex solutions to the k-Hessian curvature equations and curvature flow equations in Ω, subject to the second boundary condition Du(Ω) = Ω∗, where Ω and Ω∗ are smooth strictly convex bounded domains in R^n.
Chao Xia (Xiamen University)
Title: Stable Bernstein theorem for anisotropic minimal hypersurfaces
Abstract: The stable Bernstein theorem asks whether a complete, two-sided, stable minimal hypersurfaces in R^n is flat and it has been solved for $3\le n\le 6$. In this talk, we discuss the analog problem in anisotropic setting. We prove that a complete, two-sided, stable anisotropic minimal hypersurfaces in R^5 or R^6 is flat provided the parametric elliptic integrand is close to area functional.
This is joint work with Jia Li.
Lu Xu (Hunan University)
Title: Some new results on constant rank theorem
Abstract: In this talk, we first introduce the classical constant rank theorem(CRT). Then we give some new progress on CRT. Part of the results are about the "strengthened” versions for semi-linear elliptic equation in n-dimensional Euclidean space, by which we can deduce a rigidity theorem of the solution to the generalized Liouville equation from conformal geometry. Another part of the results concerns the generalized constant rank theorem in hyperbolic space, and we apply them to solve the Christoffel-Minkowski type Problem in this space.
Wenjiao Yan (Beijing Normal University)
Title: Complex structures and isoparametric foliations
Abstract: In this talk, we will introduce our construction of complex structures on two families of isoparametric hypersurfaces and two families of focal submanifolds in spheres. In the same time, we will explain their relations with the Hopf problem, Calabi problem and Yau problem.
This talk is based on joint work with Professor Zizhou Tang and Professor Chao Qian.
Mingwei Zhang (Freiburg University)
Title: Stability of spinorial Sobolev inequalities on S^n
Abstract: In this talk we consider spinorial Sobolev inequalities on S^n. From the variation point of view, this is a spinorial analogy of Yamabe problem. It is well known that the optimal Sobolev constant is the so-called Bär-Hijazi-Lott invariant which, as the Yamabe invariant, attains its maximum at round sphere. In this talk, we will prove on S^n that the Sobolev quotient being close to the optimal constant implies that spinor being close to an optimizer, which is a Killing spinor up to a conformal transformation. As a by-product, we prove that Killing spinors are not optimizers of another spinorial Sobolev inequality, unlike expected by experts.
This is a joint work with Prof. Guofang Wang.
Xuwen Zhang (Freiburg University)
Title: Half-space Liouville-type theorems for minimal graphs with capillary boundary
Abstract: In this talk, we will talk about our recent results on minimal surface equation with capillary boundary condition. In particular, we show that any such graph whose negative part has linear growth must be flat.
This is a joint work with Guofang Wang and Wei Wei.
Chuanqiang Chen
Genggeng Huang
Florian Johne
Ernst Kuwert
Caiyan Li
Zhe Pu
Yalong Shi
Chong Song
Guofang Wang
Jiaxuan Wang
Zhizhang Wang
Wei Wei
Chao Xia
Lu Xu
Wenjiao Yan
Mingwei Zhang
Xuwen Zhang