복소기하학연구단
Speaker Xu Wang NTNU - Norwegian University of Science and Technology We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian’s partial C0-estimate.
Speaker Ming Xiao UCSD Bounded symmetric domains are an important class of geometric objects in complex analysis and geometry, which possess a high degree of symmetry. They often serve as the model cases in the study of many rigidity phenomena. In this talk, we will discuss two mapping problems between bounded symmetric domains …
Speaker Pak Tung Ho Sogang University In this talk, I will explain what the weighted Yamabe problem is, and mention some related results that Jinwoo Shin (KIAS) and I obtained.
Speaker Aeryeong Seo Kyungpook National University TBA
Speaker Jihun Yum IBS-CCG For a bounded domain Ω in Cn, let P(Ω) be the set of all (real) probability distributions on Ω. Then, in general, P(Ω) becomes an infinite-dimensional smooth manifold and it always admit a natural Riemannian pseudo-metric, called the Fisher information metric, on P(Ω). Information geometry studies a finite-dimensional submanifold …
Speaker Hoseob Seo IBS CCG In L2 extension theorems from a singular hypersurface in a complex manifold, important roles are played by certain measures such as the Ohsawa measure which determine when a given function can be extended. We show that the singularity of the Ohsawa measure can be identified in terms of …
Speaker Gunhee Cho UCSB By exploiting the upper semicontinuity of the Kobayashi-Eisenman pseudo volume (and pseudometric) under deformations of complex structures, we establish the non-measure hyperbolicity of K3 surfaces—which M. Green and P. Griffiths verified for certain cases in 1980—holds for all K3 surfaces. Our result provides a stronger condition than the Kobayashi …
Speaker Takayuki Koike (Osaka Metropolitan University) In this talk, we explain our results on some variants of Ueda's lemma on L∞-estimates for Cech coboundary operators that hold uniformly for all flat holomorphic line bundles on compact Kähler manifolds. This talk is partially based on joint work with Y. Hashimoto and T. Uehara.Title : …
Speaker Seungjae Lee IBS CCG In this talk, we investigate the L2-Dolbeault cohomology of the symmetric power of cotangent bundles of ball quotients with finite volume, as well as their toroidal compactification. As a result, we establish a version of L2-Hodge decompostion for complex hyperbolic space forms with finite volume, under some mild …
Speaker Jiewon Park KAIST Various monotonicity formulae have profound applications in many different problems in geometric analysis. Quite often these formulae can be derived from pointwise Hessian estimates, also known as Li-Yau-Hamilton estimates or matrix Harnack inequalities. In this talk we will focus on this connection building upon Hessian estimates for the Green …
Speaker Xiaojun Huang Rutgers Univ Let M be a smooth real codimension two compact submanifold in a Stein manifold. We will prove the following theorem: Suppose that M has two elliptic complex tangents and suppose CR points are non-minimal. Assume further that M is contained in a bounded strongly pseudoconvex domain. Then M …
Speaker David Sykes IBS CCG The basic problem of finding (local) biholomorphisms mapping one real hypersurface in a complex space onto another is only well understood for a limited class of hypersurfaces, and has a fundamental relationship to their induced CR geometries. Following a light historical survey of major results in the area, …