André Arroja Neves

Department of Pure Mathematics

Imperial College London

South Kensington Campus, London SW7 2AZ, UK 

E-mail: aneves@imperial.ac.uk (short version) or a.da-silva-graca-arroja-neves@imperial.ac.uk (long version)

Teaching

Geometry of curves and surfaces M3P 5-2013  

Research

Scalar Curvature

• Classification of prime 3-manifolds with sigma-invariant greater than RP^3, (joint with H. Bray), Annals of Mathematics, 159 (2004), 407-424, pdf-file.

• Classification of all 3-manifods with Yamabe invariant greater than RP^3, (joint with K. Akutagawa),  J. Differential Geom.  75  (2007),  359--386, pdf-file.

• Area-minimizing projective planes in three-manifolds,  (joint with H. Bray, S. Brendle, M. Eichmair),  Comm. Pure Appl. Math.  63  (2010), 1237–1247, pdf-file.

• Rigidity of area-minimizing two-spheres in three manifolds,  (joint with H. Bray, S. Brendle),  Comm. Anal. Geom.  18  (2010),  821–830, pdf-file.

• Deformations of the hemisphere that increase scalar curvature,  (joint with S. Brendle, F. C. Marques),  Invent. Math.  183,  (2011),  pdf-file.

Min-Max Theory

• Rigidity of min-max minimal spheres in three-manifolds,   (joint with F. C. Marques),  to appear in Duke Math. J., pdf-file.

• Min-max theory and the Willmore Conjecture,   (joint with F. C. Marques),  to appear in Annals of Mathematics., pdf-file.

• Min-max theory and the energy of links,   (joint with I. Agol, F. C. Marques),  preprint, pdf-file.  

Mean Curvature Flow

• Singularities of Lagrangian mean curvature flow: zero-Maslov class case,  Invent. Math.  168  (2007), 449--484,  pdf-file.

• Singularities of Lagrangian mean curvature flow: monotone case, Math. Res. Lett. 17 (2010) 109--126, pdf-file.

• Translating solutions to Lagrangian mean curvature flow, (joint with G. Tian), to appear in Trans. of AMS. pdf-file.

• Finite time singularities for Lagrangian mean curvature flow,  to appear in Annals of Mathematics, 177 (2013),  pdf-file.

• Recent Progress on Singularities of Lagrangian Mean Curvature Flow, to appear on volume celebrating Prof. Schoen's 60th birthday. pdf-file.

General Relativity

•  Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds I, (joint with G. Tian),  Geom. Funct. Anal. 19 (2009), 910--942, pdf-file.

• Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds, J. Differential Geom. 84 (2010), 191--229, pdf-file.

• Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds II, (joint with G. Tian), J. Reine Angew. Math. 641 (2010)  69--93, pdf-file.