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), to
appear in JDG, pdf-file.
- Weyl Law for the Volume
Spectrum, (joint with Y. Liokumovich and F. C. Marques), to appear in
Ann. of Math, pdf-file.
- Denseness of minimal
hypersurfaces for generic metrics, (joint
with K. Irie and F. C. Marques), to
appear Ann. of Math,
pdf-file.
- Equidistribution
of minimal hypersurfaces for generic metrics, (joint
with F. C. Marques and A. Song), 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, Ann. of
Math. 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.
- On short time existence for the
planar network flow, (joint
with T. Ilmanen and F. Schulze), to appear in
JDG, 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.