2023年WilliamHill中文官方网站物理与几何演化过程研讨会
会议手册
会议服务指南
一、会议时间：2023年7月10日至7月14日，10日报到，11日-13日学术会议，7月14日离会。
二、会议地点：英国威廉希尔公司南阶梯教室
三、用餐时间：早餐—7:00-8:00， 午餐—12:00-14:00，
晚餐—18:00-20:00
地点：中州颐和酒店。
四、会议联系人：
叶嵎林：Email: ylye@vip.henu.edu.cn, Tel: 15938520926。
五、会议联系群二维码：
会议日程安排
7月10日
时间 |
内容 |
地点 |
14:30-20:00 |
会议代表报到 |
中州颐和酒店 |
18:00-20:00 |
晚餐 |
中州颐和酒店 |
7月11日
地点：英国威廉希尔公司南阶梯教室
开幕式 |
时间 |
主持人 |
事项 |
8:00-8:20 |
韩小森 |
开幕式 |
8:20-8:30 |
合 影 |
学术报告 |
时间 |
主持人 |
报告人 |
报告题目 |
8:30-9:20 |
冯淑霞 |
马力 （北京科技大学） |
极小曲面流的新进展 |
9:20-10:10 |
张振雷 （首都师范大学） |
Heat Equation Approach to Demailly Regularity Theorem |
10:10-10:30 |
茶歇 |
10:30-11:20 |
张希 |
彭锐 （浙江师范大学） |
Asymptotic behavior of the principal eigenvalue of a linear second order elliptic operator with large advection and general boundary conditions |
11:20-12:10 |
王荣年 （上海师范大学） |
Hyperdissipative Navier-Stokes Equations Driven by Time-dependent Forces: Invariant Manifolds |
12:10-14:00 |
午餐（中州颐和酒店） |
14:20-15:10 |
黄勇 |
王志强 （犹他州立大学) |
Coupled nonlinear elliptic equations with mixed couplings |
15:10-16:00 |
郭常予 （山东大学数学与交叉科学研究中心） |
Regularity of harmonic maps and generalizations |
16:00-16:20 |
茶歇 |
16:20-17:10 |
郭千桥 |
王小六 （东南大学） |
The anisotropic curvature flow in the plane |
17:10-18:00 |
张彦龙 （南开大学陈省身数学研究所） |
A discrete Gage inequality and an area-preserving crystalline flow |
18:20-20:00 |
晚餐（中州颐和酒店） |
7月12日
地点：英国威廉希尔公司南阶梯教室
学术报告 |
时间 |
主持人 |
报告人 |
报告题目 |
8:00-8:50 |
吴可 |
梁兴 （中国科学技术大学） |
扩散系统传播现象的反射对称性和非对称性 |
8:50-9:40 |
殷浩 （中国科学技术大学） |
Ricci flow on surfaces from rough initial data |
9:40-10:00 |
茶歇 |
10:00-10:50 |
郑宇 |
李东升 （西安交通大学） |
Periodic solutions of fully nonlinear elliptic equations |
10:50-11:40 |
娄本东 （上海师范大学） |
Mean curvature flows in cylinders with unbounded boundary slopes |
12:10-14:00 |
午餐（中州颐和酒店） |
14:20-15:10 |
徐兴旺 |
潘生亮 （同济大学） |
On the Decreasing Flow of isoperimetric Ratio for Embedded Closed Plane Curves |
15:10-16:00 |
邱红兵 （武汉大学） |
Bernstein type theorems of translating solitons |
16:00-16:20 |
茶歇 |
16:20-17:10 |
韩英波 |
程亮 （华中师范大学） |
On pseudolocality theorems of Ricci flows |
17:10-18:00 |
张德凯 （上海大学） |
The Monge-Ampere equation for (n-1)-quaternionic PSH functions |
18:20-20:00 |
晚餐（中州颐和酒店） |
7月13日
地点：英国威廉希尔公司南阶梯教室
学术报告 |
时间 |
主持人 |
报告人 |
报告题目 |
8:00-8:50 |
白永强 |
李向东 （中科院数学与系统科学研究院） |
On the entropy for the Porous Medium equation on Riemannian manifolds |
8:50-9:40 |
周久儒 （扬州大学） |
Ancient solutions of Ricci flow on two dimensional bad orbifolds |
9:40-10:00 |
茶歇 |
10:00-10:50 |
王中华 |
关庄丹 （WilliamHill中文官方网站） |
The existence of the Futaki-Ono k-generalized Maxwell-Einstein metric on completions of certain C* bundles |
10:50-11:40 |
马飙 （北京大学北京国际数学研究中心） |
A numerical criterion for a class of fully nonlinear equations on Kahler manifolds |
12:10-14:00 |
午餐（中州颐和酒店） |
14:20-15:10 |
叶嵎林 |
魏志强 （WilliamHill中文官方网站） |
Realizations of a compact Riemann surface with an HCMU metric into some spaces |
15:10-16:00 |
李自来 （河南理工大学） |
On non-resistive limit of 1D MHD equations with no vacuum at infinity |
16:00-16:20 |
闭幕式 |
16:20-18:00 |
自由讨论 |
18:00-20:00 |
晚餐（中州颐和酒店） |
7月14日 |
参会代表离会 |
会议报告摘要
极小曲面流的新进展
报告人：马力（北京科技大学）
报告摘要：We consider the existence problem of the minimal surface flow. We show Lebesgue space stability property of the planes along the minimal surface flow. We also study one dimensional minimal surface flow. After introducing the translating solution, we study the asymptotic behavior of the global flow. Some questions are posed for the minimal surface system flows.
Heat Equation Approach to Demailly Regularity Theorem
报告人：张振雷（首都师范大学）
报告摘要：Demailly regularity theorem of positive (1,1) currents is an important technique in pluripotential theory. In the talk I will present a heat equation approach to the regularity theorem. Some applications to Holder regularity of complex Monge-Ampere equation will also be discussed. It is a joint work with a student Lei Zhang.
Asymptotic behavior of the principal eigenvalue of a linear second order elliptic operator with large advection and general boundary conditions
报告人：彭锐（浙江师范大学）
报告摘要：In this talk, I shall report our recent progress on the principal eigenvalue of a linear second order elliptic operator with divergent form complemented by the Dirichlet boundary condition or a general Robin boundary condition. In the higher dimensional case, under proper conditions on the advection function, we establish the asymptotic behavior of the principal eigenvalue as the advection coefficient converges to infinity, and in one dimensional case, we obtain a complete description for such asymptotic behavior provided the derivative of the advection function changes sign at most finitely many times.
Hyperdissipative Navier-Stokes Equations Driven by Time-dependent Forces: Invariant Manifolds
报告人：王荣年（上海师范大学）
报告摘要：We consider in this talk the incompressible hyperdissipative Navier-Stokes equations on a 2D or 3D periodic torus, where the hyperdissipative is considered and the forcing function $f$ is time-dependent. We intend to reveal how the fractional dissipation and the time-dependent force affect long-time dynamics of weak solutions. More precisely, we prove that with certain conditions on $f$, there exists a finite-dimensional Lipschitz manifold in the L^2-space of divergent-free vector fields with zero mean. The manifold is locally forward invariant and pullback exponentially attracting. Moreover, the compact uniform attractor is contained in the union of all fibers of the manifold. In our result, no large viscosity $\epsilon$ is assumed. It is also significant that in the 3D case the spectrum of the fractional Laplacian (-Delta)^{3/2} does not have arbitrarily large gaps.
Coupled nonlinear elliptic equations with mixed couplings
报告人：王志强（ Utah State University）
报告摘要：We survey works on a class of coupled nonlinear elliptic equations with mixed couplings, in particular on classification of positive solution structure of existence and qualitative property of positive solutions. Depending upon the system being attractive or repulsive, solutions may tend to be component-wisely synchronized or segregated. We then report results on the effect of mixed coupling for which coexistence of synchronization and segregation may occur, in particular, we examine the asymptotic behavior of least energy solutions for large and small mixed coupling of multi-scales.
Regularity of harmonic maps and generalizations
报告人：郭常予（山东大学数学与交叉科学研究中心）
报告摘要：In this talk, we shall review the basic regularity theory of harmonic maps into manifolds. Then we shall introduce the recent generalization of the theory to polyharmonic maps and metric measure spaces.
The anisotropic curvature flow in the plane
报告人：王小六（东南大学）
报告摘要：In this talk, we investigate the anisotropic curvature flows with nonlocal constraint in the plane, including the area-preserving flow and the gradient flow of isoperimetric-ratio. We try to use the notion of ‘anisotropic curvature’ to convert the problem to a parabolic type PDE, and then use the method of studying isotropic flows to show the global convergence of the flow to a Wullf shape as time goes to infinity.
A discrete Gage inequality and an area-preserving crystalline flow
报告人：张彦龙（南开大学陈省身数学研究所）
报告摘要：In this talk, a discrete Gage’s inequality will be given. As its application, an area-preserving crystalline flow is considered to deform one polygon $P_{0}\in\mathcal{P}$ into another one $\widetilde{P}\in\mathcal{P}$, where $\mathcal{P}$ is defined as a class of polygons.
扩散系统传播现象的反射对称性和非对称性
报告人：梁兴（中国科学技术大学）
报告摘要：在我们以前的工作中，曾经利用二阶线性常微分方程的李雅普诺夫指数证明了KPP型反应扩散方程传播现象的对称性。在这里我们介绍问题的另一面：对于另重要一类型的反应扩散方程系统：强竞争系统，传播现象是非反射对称的。在这一工作中，我们利用的主要工具仍然是抛物方程的比较原理，但我们引入了新的上下解构造方法，我们称之为几何构造法。
Ricci flow on surfaces from rough initial data
报告人：殷浩（中国科学技术大学）
报告摘要：In this talk, we discuss the Ricci flow on surfaces with Radon measures as initial data. We also talk about the possible applications of such flows. This is based on joint work with P. Topping.
Periodic solutions of fully nonlinear elliptic equations
报告人：李东升（西安交通大学）
报告摘要：In this talk, we will mainly study the existence and uniqueness of periodic solutions of fully nonlinear elliptic equations in the whole spaces as the righthand sides are periodic functions. Here the uniqueness means a kind of Liouville type theorem.
Mean curvature flows in cylinders with unbounded boundary slopes
报告人：娄本东（上海师范大学）
报告摘要：I will talk about some mean curvature flows in cylinders, which arise in geometry and in singular limit problems of Allen-Cahn equations. I will focus on the problems with unbounded boundary slopes, including (1) 1D problem where the flow will converges to a grim reaper; (2) the nD radial problem where the flow (as well as its velocity and its gradients) tends to infinity at infinite time, while the mean curvature remain bounded.(joint works with Xiaoliu Wang and Lixia Yuan).
On the Decreasing Flow of isoperimetric Ratio for Embedded Closed Plane Curves
报告人：潘生亮（同济大学）
报告摘要：The evolution behaviour of smooth embedded closed plane curves under the descending flow of isoperimetric ratio will be presented. By giving an analogue to Huisken's distance comparison principle for initial curves with local total curvature greater than or equal to $-\pi$, it is proved that the embeddedness of the evolving curve can be preserved and singularities in finite time can be excluded during the evolution process. Moreover, it can be proved that the evolving curve will become more and more convex and converge to a circle finally as time goes to infinity.
Bernstein type theorems of translating solitons
报告人：邱红兵（武汉大学）
报告摘要：In this talk, we shall discuss Bernstein type results of translating solitons of the mean curvature flow. One special class of translating solitons with higher codimension is the symplectic translating solitons, which are solutions to symplectic MCFs, we obtain a rigidity result of symplectic translating solitons via the complex phase map, which indicates that if the cosine of the Kähler angle has a positive lower bound, then any complete symplectic translating soliton with nonpositive normal curvature has to be an affine plane. In general, we study the translating solitons via the Gauss map, and we prove a Bernstein type theorem for complete translating solitons, whose images of their Gauss maps are contained in an appropriate neighborhood of the Grassmannian manifold.
On pseudolocality theorems of Ricci flows
报告人：程亮（华中师范大学）
报告摘要：Pseudolocality theorems are one of fundamental tools in the study of Ricci flows and Riemannian geometry. In this talk we will briefly introduce previous versions of pseudolocality theorems of Ricci flows. Then we will introduce our works about pseudolocality theorems of Ricci flows for incomplete or unbounded curvature case.
The Monge-Ampere equation for (n-1)-quaternionic PSH functions
报告人：张德凯（上海大学）
报告摘要：In this talk, we consider the quaternionic Monge-Ampere equation for (n-1)-quaternionic plurisubharmonic (psh) functions. We prove the existence of the smooth solution on a compact hyperKahler manifold and thus obtain the smooth solution to the quaternionic form-type equation. This is a joint work with Prof. Jixiang Fu and Xin Xu.
On the entropy for the Porous Medium equation on Riemannian manifolds
报告人：李向东（中科院数学与系统研究院）
报告摘要：In this talk, I will present some recent results on the entropy formula for the Porous Medium equation on Riemannian manifolds.
Ancient solutions of Ricci flow on two dimensional bad orbifolds
报告人：周久儒（扬州大学）
报告摘要：In this talk, we will give a report on recent progress of a joint work with Prof. Bonnett Chow and Peng Lu, which is the classification of ancient solutions of Ricci flow on 2-dim bad orbifolds.
The existence of the Futaki-Ono k-generalized Maxwell-Einstein metric on completions of certain C* bundles
报告人：关庄丹（WilliamHill中文官方网站）
报告摘要：We prove that in every K\"ahler class on completion of certain C* bundle, there exist at least one Futaki-Ono k-generalized Maxwell-Einstein metric. This is a joint work with my Ph. D. student Jing Chen.
A numerical criterion for a class of fully nonlinear equations on Kahler manifolds
报告人：马飙（北京大学北京国际数学研究中心）
报告摘要：We consider a class of fully nonlinear equations on compact Kahler manifolds which includes the J-equation and inverse k-Hessian equations. We prove 2 criterions for the solvability of such equations. The analytic criterion tells the equivalence of the existence of subsolutions and solutions. The numerical criterion establishes a stability-existence correspondence in analogy with the J-equation and J-stability. This is a joint work with Prof. Hao Fang.
Realizations of a compact Riemann surface with an HCMU metric into some spaces
报告人：魏志强
报告摘要：In this talk, we will introduce some results about isometric realization of a compact Riemann surface with an HCMU metric into some Riemannian spaces. These works are joint with the Prof. Yingyi Wu.
On non-resistive limit of 1D MHD equations with no vacuum at infinity
报告人：李自来（河南理工大学）
报告摘要：In this paper, the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity is considered, but the initial vacuum can be permitted inside the region. By deriving a priori ν (resistivity coefficient)-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data. Moreover, as a by-product, the global well-posedness of strong solutions for the compressible resistive MHD equations is also established.
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