André Arroja Neves

Professor of Mathematics

Department of  Mathematics

University of Chicago 

 

 

 

 

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), 175-197 pdf-file.

 

 

 

Min-Max Theory

 

• Rigidity of min-max minimal spheres in three-manifolds,  (joint with F. C. Marques),  Duke Math. J. 161  (2012), 2725-2752, pdf-file. 

• Min-max theory and the Willmore Conjecture,   (joint with F. C. Marques),  Ann. of Math. 179 (2014),  683-782, pdf-file.

• Min-max theory and the energy of links,  (joint with I. Agol, F. C. Marques),  J. Amer. Math. Soc. 29 (2016), 561-578, pdf-file.

• Existence of infinitely many minimal hypersurfaces in positive Ricci curvature,  (joint with F. C. Marques),  to appear in Inventiones, pdf-file.

• New applications of Min-max Theory,  Proceedings of International Congress of Mathematics} (2014), 939-957,  pdf-file.

• The Willmore Conjecture,  (joint with F. C. Marques),  Jahresber. Dtsch. Math.-Ver. 116 (2014), 201-222 ,  pdf-file.

• Applications of Almgren--Pitts Min-max Theory,  (joint with F. C. Marques),  Current developments in mathematics 2013}, 1-71, Int. Press, Somerville, MA, 2014, pdf-file.
• Morse index and multiplicity of min-max  minimal hypersurfaces, (joint with F. C. Marques), To appear in Cambridge. Journ. of Mathematics, pdf-file.
• The catenoid estimate and its geometric applications, (joint with D. Ketover and F. C. Marques), preprint, pdf-file.
• Weyl Law for the Volume Spectrum, (joint with Y. Liokumovich and F. C. Marques), submitted, 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),  Trans. Amer. Math. Soc. 365  (2013), 5655-5680, pdf-file.

• Finite time singularities for Lagrangian mean curvature flow,  Annals of Mathematics,  177  (2013), 1029-1076,  pdf-file.

• Recent Progress on Singularities of Lagrangian Mean Curvature Flow, Surveys in Geometric Analysis and Relativity, ALM 20  (2011) 413--436, pdf-file.

• Uniqueness of self-expanders,  (joint with J. Lotay), Geom. Topol. 17 (2013), 2689-2729, 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.
• The Penrose inequality for asymptotically locally hyperbolic spaces with nonpositive mass, (joint with D. Lee), Comm. Math. Phys. 339 (2015), 327-352,  pdf-file.