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几何分析讨论班

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20

2023-09

Phase transitions with Allen-Cahn mean curvature bounded in Lp.

Title: Phase transitions with Allen-Cahn mean curvature bounded in Lp. Abstract: We consider the varifolds associated to a phase transition problem whose first variation of Allen-Cahn energy is Lp integrable with respect to the energy measure. We can see that the Dirichlet and potential part of the energy are almost equidistributed. After passing to the phase field limit, one can obtain...

20

2023-09

Sobolev inequalities and regularity of the linearized complex MongeAmp\`ere and Hessian equations

报告人：王嘉项博士（南开大学），题目：Sobolev inequalities and regularity of the linearized complex MongeAmp\`ere and Hessian equations摘要：Let $u$ be a smooth, strictly $k$-plurisubharmonic function on a bounded domain $\Omega\in\mathbb C^n$ with $2\leq k\leq n$.In this talk, we will discuss the regularity of solution to the linearized complex Monge-Amp\`ere and Hessian equations when the...

20

2023-09

Singularity Type for Kahler-Ricci Flow over Minimal Manifolds

报告人：张州教授（悉尼大学）时间：2023年9月18日（星期一）下午16:00-17:00 地点：海纳苑2幢102摘要： in this talk, we start by describing the history of the study on this Kahler-Ricci flow, usually considered as the easy-sign version. The degenerate setting has been the main interest for the past 2 decades, following Tian’s Program which was later elaborated as Analytic Minimal Model Prog...

20

2023-09

几何分析讨论班--Mean field type equations and some related problems

报告人：胡烨耀教授（中南大学）时间：2023年9月25日（星期一）下午16:00-17:00 地点：海纳苑2幢102摘要：In this talk, we will first review the resolution of the celebrated Chang-Yang’s conjecture on a sharp Moser-Trudinger type inequality on the two-dimensional sphere. Then we recall the complete theory in dimension one and emphasize the key role played by mean field type equations. Moreover, h...

30

2023-05

A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation

Title: A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equationAbstract: The deformed Hermitian-Yang-Mills equation is a fully nonlinear elliptic PDE on Kahler manifolds, which can be regarded as the complex analogue of the Lagrangian equation. In this talk, I will present a Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation, wh...

25

2023-05

Some rigidity theorems on conformal deformation

题目: Some rigidity theorems on conformal deformation报告人：来米加长聘副教授（上海交通大学）时间：6月1日，10:30-11:30地点：海纳苑2幢202摘要: In this talk, I shall discuss some rigidity theorems on conformal deformations. The main discovery here is that on a complete noncompact manifold with suitable curvature assumption, then one cannot increase the Schouten tensor via conformal deformation. The...

04

2023-04

Fully non-linear elliptic equations on compact almost Hermitian manifolds

报告人：黄立鼎（西湖大学）时间：2023年3月10日星期五上午 10:00地点：紫金港校区海纳苑2幢101室摘要: We will talk about a priori estimates for solutions of a general class of fully non-linear equations on compact almost Hermitian manifolds. As an application, we will solve the complex Hessian equation and the Monge--Ampère equation for (n-1)-plurisubharmonic equations in the almost Hermitian setting....

24

2020-12

Geometry&Analysis| Mean curvature flow with Type-II curvature blow up

报告人：吴昊天 (悉尼大学)报告时间：2020年12月24日（周四）下午2:30-4:30报告地点：腾讯会议ID：248 180 972；无密码链接：https://meeting.tencent.com/s/c1ixUuIEoRyp报告摘要: Mean curvature flow deforms a hypersurface in a given ambient space in the direction of its mean curvature vectors. In this talk, we present some results on mean curv...

24

2020-11

Geometry&Analysis| 规范场论中的几何反问题

报告人：陈曦(剑桥大学)时间：2020年12月18日（周五）下午3:30-5:30线上报告：腾讯会议ID：596 110 736密码：1812链接：https://meeting.tencent.com/s/YbaZtqZF008R摘要：在粒子物理中，粒子的相互作用可以由各类欧拉-拉格朗日方程的解刻画。这类方程本质上，是时间依赖的非交换非线性波方程。我们将关注粒子物理标准模型中描述规范玻色子强、弱、电磁相互作用的杨-米尔斯方程，讨论从局部可测量的信息探测规范玻色子的唯一性问题...

24

2020-11

Geometry&Analysis | Solvability of a class of singular fourth order equations of Monge-Ampère type

报告人：周斌(北京大学)时间：2020年12月4日（周五）下午3：00-5：00地点：线上报告：腾讯会议 ID：917 693 185密码：0412链接：https://meeting.tencent.com/s/4Zn0WaQ9uHv2 摘要：We study the solvability of the second boundary value problem for a class of highly singular fourth order equations of Monge-Ampere type. They arise in the approximation of convex functionals subject to a convexity const...

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