4th Geometry Day

Schedule

• TBA

Title & Abstract

• Jihyeon Lee (IBS-CGP) 

Title : Rigidity of three-manifolds via the magnetically charged Hawking mass

Abstract : For a two-sided, compact, embedded and strictly stable minimal surface that locally maximizes the magnetically charged Hawking mass, we establish a local rigidity result within a time-symmetric initial data set for the Einstein--Maxwell equations with both electric and magnetic charges and a negative cosmological constant. In particular, we show that a neighborhood of the surface is isometric to the dyonic Riessenr--Nordstr\"{o}m--Anti-de Sitter space. Furthermore, we derive an area estimate for the surface expressed in terms of its topology and the relevant physical constrains.

• Sanghun Lee (Pusan National University) 

Title : Rigidity of initial data sets with boundary

Abstract: In this talk, we explore the rigidity of initial data sets with boundary in the case where a marginally outer trapped surface with a capillary boundary is embedded in the initial data set. We begin by introducing the notions of an initial data set and a marginally outer trapped with a capillary boundary, and then establish the rigidity of three-dimensional initial data sets with boundary. Finally, we extend these results to prove the rigidity of high dimensional initial data sets.

• Jungwoo Moon (Chung-Ang University) 

Title : Weyl curvature properties of divergence-free traceless Ř tensor

Abstract : In this talk, we study a complete divergence of Weyl curvature with divergence-free traceless \check{R} curvature. Specifically, an another formula of the third order divergence of Weyl curvature is calculated. Also, some rigidity properties of Ricci soliton would be proved. 

• Jooyeon Park (Sookmyung Women's University) 

Title : Stability of minimal hypersurfaces under angle function constraints in warped product manifolds

Abstract : In 2016, Aledo and Rubio showed that every complete noncompact two-sided minimal surface with positive angle function is stable when immersed in a three-dimensional warped product manifold with a positive warping function whose second derivative is nonnegative. This condition on the angle function is satisfied, for instance, when the surface is locally given as a graph. Inspired by their work, in this talk we discuss the higher-dimensional extension of this result. As an application, this yields that complete oriented noncompact hypersurfaces in Euclidean and hyperbolic spaces, which can be locally represented as minimal graphs, are stable.

• Wonjoo Lee (Korea University) 

Title : Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space

Abstract : In this talk, we will present a result on the value distribution of the Gaussian curvature of complete spacelike constant mean curvature surfaces in the isotropic 3-space I3, which is closely related to a Bernstein-type theorem in I3.

• Kiyoon Eum (KAIST) 

Title : Intro to Kahler geometry and Bergman kernel

Abstract : I will introduce Kahler geometry and Bergman kernel on compact Kahler Hodge manifolds. Then I will explain how they are related and talk about my recent results.