Selected Publications

Simon Brendle

Research Monograph

Ricci Flow and the Sphere Theorem, Graduate Studies in Mathematics, volume 111, American Mathematical Society (2010)
Table of Contents   Preface   Chapters 1 and 2
Review by Professor Klaus Ecker, Jahresbericht der Deutschen Mathematiker-Vereinigung
Review by Professor Huy The Nguyen, Bulletin of the London Mathematical Society

Geometry of Hypersurfaces and the Lawson Conjecture

  • Embedded minimal tori in S^3 and the Lawson conjecture, to appear in Acta Mathematica abstract
    • A background discussion of the Lawson Conjecture can be found here: The 12th Problem by Professor Paul Norbury, Australian Mathematical Society Gazette
  • A sharp bound for the area of minimal surfaces in the unit ball, Geometric and Functional Analysis 22, 621--626 (2012) abstract
  • Constant mean curvature surfaces in warped product manifolds, to appear in Publications Mathématiques de l'IHÉS abstract
  • Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, to appear in Journal of Differential Geometry (joint with M. Eichmair) abstract
  • A Minkowski-type inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold, preprint (joint with P.K. Hung and M.T. Wang) abstract
  • Uniqueness results for minimal surfaces and constant mean curvature surfaces in Riemannian manifolds, to appear in Proceedings of the European Congress of Mathematicians 2012

    • Uniqueness of Ricci Solitons

  • Rotational symmetry of self-similar solutions to the Ricci flow, to appear in Inventiones Mathematicae abstract
  • Rotational symmetry of Ricci solitons in higher dimensions, preprint abstract

    • Ricci Flow and the Differentiable Sphere Theorem

  • Manifolds with 1/4-pinched curvature are space forms, Journal of the American Mathematical Society 22, 287--307 (2009) (joint with R. Schoen) abstract
  • Classification of manifolds with weakly 1/4-pinched curvatures, Acta Mathematica 200, 1--13 (2008) (joint with R. Schoen) abstract
  • A general convergence theorem for the Ricci flow in higher dimensions, Duke Mathematical Journal 145, 585--601 (2008) abstract
  • A generalization of Hamilton's differential Harnack inequality for the Ricci flow, Journal of Differential Geometry 82, 207--227 (2009) abstract
  • Sphere theorems in geometry, Surveys in Differential Geometry, volume XIII, 49--84 (2009) (joint with R. Schoen) abstract
  • Einstein manifolds with nonnegative isotropic curvature are locally symmetric, Duke Mathematical Journal 151, 1--21 (2010) abstract
  • A note on Ricci flow and optimal transportation, Journal of the European Mathematical Society 13, 249--258 (2011) abstract
  • Ancient solutions to the Ricci flow with pinched curvature, Duke Mathematical Journal 158, 537--551 (2011) (joint with G. Huisken and C. Sinestrari) abstract
  • Riemannian manifolds of positive curvature, Proceedings of the International Congress of Mathematicians 2010, volume I, pp. 449--475 (joint with R. Schoen) abstract
  • Curvature, sphere theorems, and the Ricci flow, Bulletin of the American Mathematical Society 48, 1--32 (2011) (joint with R. Schoen) abstract
  • Evolution equations in Riemannian geometry, Japanese Journal of Mathematics 6, 45--61 (2011) abstract

    • The Yamabe Problem

  • Convergence of the Yamabe flow for arbitrary initial energy, Journal of Differential Geometry 69, 217--278 (2005) abstract
  • Elliptic and parabolic problems in conformal geometry, Proceedings of the International Congress of Mathematicians 2006, volume II, pp. 691--704
  • A short proof for the convergence of the Yamabe flow on S^n, Pure and Applied Mathematics Quarterly 3, 499--512 (2007) abstract
  • Convergence of the Yamabe flow in dimension 6 and higher, Inventiones Mathematicae 170, 541--576 (2007) abstract
  • Blow-up phenomena for the Yamabe equation, Journal of the American Mathematical Society 21, 951--979 (2008) abstract
  • Blow-up phenomena for the Yamabe equation II, Journal of Differential Geometry 81, 225--250 (2009) (joint with F.C. Marques) abstract
  • On the conformal scalar curvature equation and related problems, Surveys in Differential Geometry, volume XII, 1--19 (2008) abstract
  • An existence theorem for the Yamabe problem on manifolds with boundary, preprint (joint with S. Chen) abstract
  • Recent progress on the Yamabe problem, Surveys in Geometric Analysis and Relativity, Advanced Lectures in Mathematics volume 20, pp. 29--47 (joint with F.C. Marques) abstract

    Complex and Special Lagrangian Geometry

  • Minimal Lagrangian diffeomorphisms between domains in the hyperbolic plane, Journal of Differential Geometry 80, 1--22 (2008) abstract
  • A boundary value problem for minimal Lagrangian graphs, Journal of Differential Geometry 84, 267--287 (2010) (joint with M. Warren) abstract
  • On the Lagrangian minimal surface equation and related problems, to appear in Surveys in Differential Geometry abstract
  • Ricci flat Kähler metrics with edge singularities, to appear in International Mathematics Research Notices abstract

    • Scalar Curvature Rigidity and Min-Oo's Conjecture

  • Area-minimizing projective planes in three-manifolds, Communications on Pure and Applied Mathematics 63, 1237--1247 (2010) (joint with H. Bray, M. Eichmair, and A. Neves) abstract
  • Rigidity of area-minimizing two-spheres in three-manifolds, Communications in Analysis and Geometry 18, 821--830 (2010) (joint with H. Bray and A. Neves) abstract
  • Deformations of the hemisphere that increase scalar curvature, Inventiones Mathematicae 185, 175--197 (2011) (joint with F.C. Marques and A. Neves) abstract
  • Scalar curvature rigidity of geodesic balls in S^n, Journal of Differential Geometry 88, 379--394 (2011) (joint with F.C. Marques) abstract
  • Rigidity phenomena involving scalar curvature, Surveys in Differential Geometry, volume XVII, 179--202 (2012) abstract

    • Q-Curvature

  • Global existence and convergence for a higher order flow in conformal geometry, Annals of Mathematics 158, 323--343 (2003) abstract
  • Convergence of the Q-curvature flow on S^4, Advances in Mathematics 205, 1--32 (2006) abstract

    Control Theory and Applications to Economics

  • Portfolio selection under incomplete information, Stochastic Processes and their Applications 116, 701--723 (2006) abstract
  • On a problem of optimal stochastic control with incomplete information, Applied Mathematics and Optimization 58, 257--274 (2008) abstract