Simon Brendle

Simon Brendle ( born June 1981) is a German mathematician who deals with partial differential equations in differential geometry.

Brendle won the 1995, 1996 and 1997, the national competition mathematics. It was founded in 2001 summa cum laude from the University of Tübingen with Gerhard Huisken doctorate ( curvature flows on manifolds with boundary ). 2002/2003 he worked at the Institute for Advanced Study, and then to 2005 Assistant Professor at Princeton University. From 2005 he was assistant professor and from 2008 professor at Stanford University.

He has been a visiting scientist at the ETH Zurich (2008), at the University of Cambridge, the University of Paris and at the Massachusetts Institute of Technology.

Simon Brendle constructed in 2006 counterexamples to Richard Schoen compactness assumption for the Yamabe problem. He also dealt with the Yamabe flow and its convergence behavior. In 2007 he proved with Richard Schoen the differentiable version of the spheres set ( Differentiable Sphere Theorem ). With FC Marques and André Neves he solved the conjecture of Min -Oo ( in three or more dimensions ) - it says that an n-dimensional hemisphere with scalar curvature at least n (n- 1) and a Riemannian metric in a neighborhood of edge with the standard metric matches an isometric to the standard metric Riemann metric has. The set can be considered as an analogue in the case of the sphere for the set of positivity of mass in general relativity theory. In 2012 he proved the Lawson conjecture and answered a question about the uniqueness of self-similar solutions of the Ricci flow.

In 2012 he was awarded the EMS price, and held the Euler Lecture 2012 in Sanssouci. In 2011 he was Lecturer Takagi Japanese Mathematical Society and 2006 Invited Speaker at the International Congress of Mathematicians (ICM ) in Madrid (Elliptic and Parabolic problem in conformal geometry ) and 2010 with R. Schoen on the ICM in Hyderabad ( Riemannian manifolds of positive curvature ). 2006 he was a Sloan Fellow. For 2014, he was awarded the Bôcher Memorial Prize.

Writings

  • Elliptic and parabolic problems in conformal geometry, Proceedings of the International Congress of Mathematicians (ICM 2006), Madrid, Spain, August 22 to 30, 2006. Vol II, S.691 -704, 2006
  • Blow-up phenomena for the Yamabe equation, Journal of the AMS 21, pp. 951-979, 2008
  • Ricci Flow and the Sphere Theorem, American Mathematical Society, Graduate Studies in Mathematics, Volume 111, 2010
  • With R. Schoen Riemannian manifolds of positive curvature, Proceedings of the International Congress of Mathematicians (ICM 2010), Hyderabad, India, August 19 to 27, 2010, Vol I, pp. 449-475, 2011.
  • With FC Marques, A. Neves deformation of the hemisphere did increase enlarge scalar curvature, Inventiones Mathematicae, Volume 185, 2011, p 175-197, Preprint (Min -Oo conjecture )
  • Embedded minimal tori in conjecture and the Lawson, Acta Math 211 (2013), no 2, 177-190. Preprint ( Lawson 's conjecture )
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