André Arroja Neves
Professor 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
·
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.