André Arroja Neves

Professor of Mathematics

Department of  Mathematics

University of Chicago 

 

 

 

 

Some surveys

 

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

·       Applications of Min–Max Methods to Geometry, (joint with F. C. Marques), Springer LNM, volume 2263 (2020). pdf-file

·       Minimal surface entropy of negatively curved manifolds,  (joint with D. Calegari,  and F.C. Marques), to appear in  Perspectives in Scalar Curvature, pdf-file.

 

 

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

·       Deformations of the hemisphere that increase scalar curvature,  (joint with S. Brendle, F. C. Marques), Invent. Math.  183,  (2011), 175-197 pdf-file.

 

Minimal surfaces and curvature

 

·       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.

·       Counting minimal surfaces in negatively curved 3-manifolds,  (joint with D. Calegari,  and F.C. Marques), to appear in DMJ.  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), Camb. J. Math. 4 (2016), 463-511, pdf-file.

·       The catenoid estimate and its geometric applications, (joint with D. Ketover and F. C. Marques), J. Differential Geom. 115 (2020), 1-26., pdf-file.

·       Weyl Law for the Volume Spectrum, (joint with Y. Liokumovich and F. C. Marques), Ann. of Math. 187 (2018), 933--961, pdf-file.

·       Denseness of minimal hypersurfaces for generic metrics, (joint with K. Irie and F. C. Marques), Ann. of Math. 187 (2018), 963--972, pdf-file.

·       Equidistribution of minimal hypersurfaces for generic metrics, (joint with F. C. Marques and A. Song), Invent. Math. 216 (2019), 421--443. pdf-file.

·       Morse index of multiplicity one min-max minimal hypersurfaces, (joint with F. C. Marques), Adv. Math. 378 (2021) Paper No. 107527. pdf-file

·       Applications of Min–Max Methods to Geometry, (joint with F. C. Marques), Springer LNM, volume 2263 (2020). pdf-file

·       Morse inequalities for the area functional, (joint with F. C. Marques and R. Montezuma), preprint pdf-file

·       Multiplicity one and strictly stable Allen-Cahn minimal hypersurfaces, (joint with M. Guaraco and F. C. Marques ), to appear in JDG pdf-file

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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, Ann. of Math. 177  (2013), 1029-1076,  pdf-file.

·       Uniqueness of self-expanders,  (joint with J. Lotay), Geom. Topol. 17 (2013), 2689-2729, pdf-file.

·       On short time existence for the planar network flow,  (joint with T. Ilmanen and F. Schulze), J. Differential Geom. 111 (2019), 39-89., pdf-file.

 

 

Mathematical 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.