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【IAS】Melanie Rupflin:Singularities of Teichmüller harmonic map flow
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https://www.youtube.com/watch?v=j4iTcbsxbTY 美国普林斯顿高等研究院 Topic: Singularities of Teichmueller harmonic map flow Speaker: Melanie Rupflin Affiliation: University of Oxford Date: March 4, 2019 Melanie Rupflin是一位世界著名的英国数学家,现任英国牛津大学数学副教授。她的研究是在几何和分析的交界上,她对极小曲面和几何流的研究特别感兴趣,它们将几何对象变形为最优状态。Melanie Rupflin于2010年数学博士毕业于瑞士苏黎世联邦理工学院ETH Zürich,导师为世界著名的德国数学家Michael Struwe、法国数学家Tristan Rivière和英国数学家Peter Topping。Melanie Rupflin的博士论文为《Harmonic Map Flow And Variants》。Melanie Rupflin曾在英国华威大学(The University of Warwick)、德国马克斯·普朗克引力物理学研究所和德国莱比锡大学担任博士后职位。在她的研究中,她研究描述几何问题的偏微分方程理论中的问题。她对与具有极小可能面积的曲面相关的问题特别感兴趣(给定一些约束,例如给定的边界曲线或规定的封闭体积),这些曲面在自然界中也可以看作是肥皂膜或肥皂泡。她也在研究几何流的特性,这些方程是设计用来使几何对象(例如曲面)朝着最优状态演化的方程。在过去的几年中,Melanie Rupflin在与Peter M. Topping的合作中,他们已经证明,他们在2012年定义的几何流成功地将任意流形中的任何给定曲面改变为极小曲面的集合,即该面积的minimisers(或临界点)。 Melanie Rupflin, Peter M. Topping——《Flowing maps to minimal surfaces》:https://doi.org/10.48550/arXiv.1205.6298 Melanie Rupflin, Peter M. Topping, Miaomiao Zhu——《Asymptotics of the Teichmüller harmonic map flow》:https://doi.org/10.48550/arXiv.1209.3783 Melanie Rupflin, Peter M. Topping——《Teichmüller harmonic map flow into nonpositively curved targets》:https://doi.org/10.48550/arXiv.1403.3195 Melanie Rupflin——《Teichmüller harmonic map flow from cylinders》:https://doi.org/10.48550/arXiv.1501.07552 Tobias Huxol, Melanie Rupflin, Peter M. Topping——《Refined asymptotics of the Teichmüller harmonic map flow into general targets》:https://doi.org/10.48550/arXiv.1502.05791 Melanie Rupflin, Peter M. Topping——《Global weak solutions of the Teichmüller harmonic map flow into general targets》:https://doi.org/10.48550/arXiv.1709.01881 Craig Robertson, Melanie Rupflin——《Finite-time degeneration for variants of Teichmüller harmonic map flow》:https://doi.org/10.48550/arXiv.1807.06363 James Kohout, Melanie Rupflin, Peter M. Topping——《Uniqueness and nonuniqueness of limits of Teichmueller harmonic map flow》:https://doi.org/10.48550/arXiv.1909.06422
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【系列课程】Wangjian Jian--Ricci Flow课程38
【CIRM】Melanie Rupflin:Singularities of Teichmüller harmonic map flow
【系列课程】Wangjian Jian--Ricci Flow课程37
微分几何速通!流形和张量场
Nigel Hitchin:Generalizations of Teichmüller space
微分几何速通!协变导数算符
Vishnu Mangalath:Gradient Estimates in Mean Curvature Flow——1
Aaron Naber:Nonlinear Harmonic Maps and the Energy Identity
Vishnu Mangalath:Estimates for Mean Curvature Flow in R^3
Felix Schulze:Mean curvature flow with generic initial data
Albert Wood:Singularities of Lagrangian Mean Curvature Flow——1
Richard Bamler:Mean curvature flow in R^3 and the Multiplicity One Conjecture——1
Vishnu Mangalath:Gradient Estimates in Mean Curvature Flow——2
Gunhee Cho:Calabi conjecture的Kähler-Ricci flow方法和Kähler–Einstein metric的存在
James Stanfield:Necks in Mean Curvature Flow
Anusha Krishnan:Positive sectional curvature and Ricci flow
时至今日人类终于认识了测地线?
Stepan Hudecek:Mean Curvature Flow with surgery——2
Eckhard Meinrenken:带边曲面的Teichmüller空间的辛几何——2
Ben Andrews:Ricci flow on surfaces
Adam Thompson:The Second Fundamental Form at Singularities of MCF
Richard Schoen:Steklov特征值和自由边界极小曲面
Kyeongsu Choi:Noncollpased ancient mean curvature flow——2
Yong Wei:Curvature measures and volume preserving curvature flow——3
Devesh Rajpal:Asymptotic Convexity in MCF——1
Felix Otto:The thresholding scheme for mean curvature flow
Xuwen Zhang:Volume-constraint local energy-minimizing sets in a ball——4
Alice Chang(张圣容):Conformal gap theorems of S^4 and CP^2
Gunhee Cho:Intuition on Mabuchi functional
Andreas Cap:Cartan geometries——02
Camillo de Lellis—Area-minimizing Integral Currents:Singularities&Structure
Andreas Cap:Cartan Geometries——01
Andrea Mondino:满足Ricci曲率有下界的度量测度空间(Metric Measure Space)——1
Kyle Broder:Kähler-Ricci flow and the Wu-Yau theorem——1
Andrea Mondino:Time-like Ricci curvature bounds via optimal transport
Kyle Broder:Kähler-Ricci flow and the Wu-Yau theorem——2
Karl-Theodor Sturm:度量测度空间的Distribution-valued Ricci Bounds(Metric Measure Space)
Devesh Rajpal:Asymptotic Convexity in MCF——2
Andrea Mondino:满足Ricci曲率有下界的度量测度空间(Metric Measure Space)——3
Andrea Mondino:满足Ricci曲率有下界的度量测度空间(Metric Measure Space)——2