Abstract
The study of minimal and constant mean curvature surfaces has a long tradition in differential geometry. These surfaces arise as models for soap films; constant mean curvature surfaces also play a role in connection with the isoperimetric problem. In Euclidean spaces, there are no closed minimal surfaces, and (by the famous Alexandrov) the only closed, embedded surfaces with constant mean curvature are the round spheres. However, the picture is very different when we allow curved background spaces. In this lecture, the speaker will discuss various rigidity theorems for minimal and constant mean curvature surfaces in curved background manifolds. These include a very general version of Alexandrov's theorem, and the solution of Lawson's conjecture (which classifies minimal tori in the 3-dimensional sphere).
About the speaker
Prof Brendle received his PhD in Mathematics from the Tübingen University in 2001. He became an Assistant Professor in Princeton University in 2003 and moved to Stanford University in 2005. In 2016, Prof Brendle joined Columbia University as a Professor of Mathematics.
Prof Brendle’s research focuses on differential geometry and nonlinear partial differential equations. He has achieved major breakthroughs in geometry including results on the Yamabe compactness conjecture, the differentiable sphere theorem (jointly with R Schoen), the Lawson conjecture and the Ilmanen conjecture, as well as singularity formation in the mean curvature flow, the Yamabe flow and the Ricci flow.
Prof Brendle was elected a Corresponding Member of the Heidelberg Academy of Sciences and Humanities (2017), a Senior Scholar of Clay Mathematics Institute (2014) and a Sloan Research Fellow of Alfred P Sloan Foundation (2006). He also received the Fermat Prize by the Institut de Mathématiques de Toulouse (2017), the Bôcher Memorial Prize by the American Mathematical Society (2014) and the European Mathematical Society Prize (2012).
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