Home Page of Isabel Salavessa
Isabel Salavessa (isabel.salavessa@tecnico.ulisboa.pt)
(+351)
218419105
Scientific Training
 Ph.D. in Mathematics from the University of Warwick, 1987.
Graphs with parallel mean curvature and a variational problem in
conformal geometry, adviser:
James Eells (Warwick),(Wiki)
exam committee: Nigel Hitchin (Oxford) and
David Epstein (Warwick).
Present Position
Previous Positions

Principal Investigator of Technical University of Lisbon working at
Centro de Física das Interacções
Fundamentais, at the
Instituto Superior Técnico. 19972014.
 Assistant Researcher of the Technical University of Lisbon, 19921997.
 Assistant Researcher of the Instituto Nacional de
Investigação Científica, Lisbon, 19911992.
 Visiting Researcher at the University of Maryland at College Park,
1991.
 Research Assistant of the Instituto Nacional de
Investigação Científica, Lisbon, 19881991.
 Teaching Assistant of the University of Lisbon, 19851988.
 Junior Teaching Assistant of the University of Lisbon, 19831985.
Main Research Interests
 DIFFERENTIAL GEOMETRY AND GEOMETRIC ANALYSIS.
 Submanifolds with parallel mean curvature.
 Isoperimetric inequalities and spectral geometric theory.
 BernsteinHeinzChern results for
submanifolds with parallel mean curvature.
 Submanifolds in Calibrated Geometry.
 Submanifolds of pseudoRiemannian spaces.
 Submanifolds of statistical manifolds.
 Geometric flows.
 Willmore submanifolds.
 Submanifolds in weighted spaces.
 Surfaces with Contant Mean Curvature. Variational Theories. Stability. Applications.
Selected Published Works in Scientific Journals

Heinz mean curvature estimate in warped product spaces $M\times_{e^{\psi}}N$
Annals of Global Analysis and Geometry, First Online 30 September 2017.DOI:https://doi.org/10.1007/s104550179577x, ArXiv

Dirichlet principal eigenvalue comparison theorems in geometry with torsion
(with Ana Cristina Ferreira)
Journal of Mathematical Analysis and Applications, 453 (2017) no.2, 15 September, 700723. DOI: 10.1016/j.jmaa.2017.04.030,
ArXiv (2015)

Uniqueness of $\phi$minimal hypersurfaces in warped product manifolds
(with Juan J. Salamanca) Journal of Mathematical Analysis and Applications 422 (2015), no.2, 13761389
DOI: 10.1016/j.jmaa.2014.09.028

Spherical symmetrization and the first eigenvalue of geodesic disks on manifolds
(with Pedro Freitas and Jing Mao)
Calculus of Variations and Partial Differential Equations, 51
(2014), issue 34, pp 701724;
DOI: 10.1007/s0052601306927

The isoperimetric problem in higher codimension
(with Frank Morgan)
Manuscripta Mathematica, 142 (no.34)(2013) 369382;
DOI: 10.1007/s0022901206048
[arxiv:1203.3304]

Stable 3spheres in C^3.
J. Mathematics Research, 4 , no.2 (April) 2012, 3444;
DOI: 10.5539/jmr.v4n2p34
[arxiv:1111.3287]

Stability of submanifolds with parallel mean curvature in calibrated manifolds,
Bull. Braz. Math. Soc. (NS), 41(4)(2010), 495530.
[arxiv:0911.4689]

A spectral Bernstein theorem, (with Pedro Freitas),
Ann. Mat. Pura ed Appl., 190(1)(2011),7790,
DOI: 10.1007/s1023101001390

BernsteinHeinzChern results in calibrated manifolds, (with G. Li),
Rev. Mat. Iberoam., 26(2), 2010, 651692
[arxiv:0802.0946]

Mean Curvature Flow of Spacelike Graphs, (with G. Li),
Math. Zeitschrift, 269(34) (2011), 697719,
DOI: 10.1007/s0020901007684.
[arxiv:0804.0783]

Graphic Bernstein Results in Curved PseudoRiemannian Manifolds,
( with G. Li),
Journal of Geometry and Physics 59 (9)(2009) 13061313.
DOI:10.1016/j.geomphys.2009.06.011).
 The G2sphere of a 4manifold,
(with R. Albuquerque),
Monatsh. Math., 158, No.4 (2009), 335348.
DOI 10.1007/s0060500800533.
 Erratum to: The G2sphere of a 4manifold,
(with R. Albuquerque),
Monatsh. Math., 160, No.1 (2010), 109110.
DOI 10.1007/s0060501001912.
 Forced convex mean curvature flow in Euclidean space,
(with G. Li),
Manuscripta Math. 126 (2008), 333351.
DOI 10.1007/s002290080181z.
 Spacelike graphs with parallel mean curvature,
Bull. Belgian Math. Soc. Simon Stevin 15 (1)(2008), 6576
 On the twistor space of pseudospheres, (with R. Albuquerque),
Differential Geometry and its Applications 25 (2)(2007), 207219
 Transgression forms in dimension 4, (with A. Pereira do Vale),
Int. J. Geom. Meth. Mod. Phys. 3 no. 56 (2006) 12211254.
 Spacetime formulation for curvature flow of high codimension
(with G. Li),
JP Journal of Geometry and Topology 6 no. (2006)303318.
 On the Kähler angles of submanifolds
Port. Math. (N.S.) (60) no.2 (2003), 215235.

Minimal submanifolds of KählerEinstein
manifolds with equal Kähler angles, (with G. Valli),
Pacific J.Math. 205 no.2 (2002), 197235.

Broadlypluriminimal submanifolds of KählerEinstein manifolds,
(with G. Valli),
Yokohama Math.J., (48) (2001), no.2, 181199.

On a class of graphs with prescribed mean curvature,
(with D.M. Duc),
Manuscripta Math. 82 (1994) 227234.

Willmore submanifolds of the Möbius space and a
Bernsteintype theorem, (with M. Rigoli),
Manuscripta Math. 81 (1993) 203222.

Sphericaltype hypersurfaces in a Riemannian manifold, (with
JP. Ezin and M. Rigoli),
Israel J. Math. 71 (1990)(2), 193209.

Graphs with parallel mean curvature,
Proc. Amer. Math.
Soc. 107 (1989) 449458.

Conformal and isometric immersions of Riemannian manifolds,
(with M.Rigoli)
Math. Zeitschrift 196 (1987), no.2, 293300.

Grassmannian manifolds as subsets of Euclidean spaces,
(with A. Machado), Differential geometry
(Santiago de Compostela, 1984), 85102, Res. Notes in Math.,131,
Pitman, Boston, MA, 1985.
Selected Talks Published in Proceedings

Mean Curvature Flow and BernsteinCalabi Results for Spacelike Graphs,
(with G. Li),
VIII International Colloquium on Differential Geometry,
Santiago de Compostela, Spain, 711 July 2008, satellite event of
the 5th European Congress of Mathematics, Lopez, Jesus A. Alvarez(Ed),
GarciaRio, Eduardo(Ed),World Scientific Publishing Company, April 2009,
pp. 164174,
arxiv:0810.3371

Mininal Submanifolds of KählerEinstein Manifolds without Complex
Directions and of Half Dimension, Summer School on
Differential Geometry, A.M. d'Ezevedo Breda, F.J. Craveiro de Carvalho,
J.M. Nunes da Costa, Bernd Wegner, Coimbra, 37 September 1999.
http://www.emis.de/proceedings/Coimbra99/index.html
Selected Invited Talks (not published)

Chengâ€™s type comparison results for the principal eigenvalue of a V drift Laplacian on a Riemannian manifold (with Ana Cristina Ferreira).
International Meeting AMS/EMS/SPM, 1013 June, 2015, Porto, Special Session 22 (Geometric Analysis) p. 39.
Program
abstract

Submanifolds with parallel mean curvature in calibrated manifolds:
A variational approach, Third Minho Meeting on Mathematica Physics,Universidade do Minho, Braga, November 4, 2011.

The Spectrum of Minimal Submanifolds, invited talk at Dep. Geometria
e Topologia, Universidad de Granada, Spain, 3 April 2009.

Angles of Minimal Submanifolds, invited talk at Workshop: Submanifolds
Sendai 2004, Tohoku University, Sendai Japan, February 1718, 2004.

Minimal Submanifolds of KählerEinstein Manifolds ,
invited talk at Special Session on Ricci Curvature and Related Topics,
966th AMS Meeting, Stevens Institute of Technology, Hoboken, NJ, USA,
April 2829, 2001.
Research Projects
 Fundação
para a Ciencia e Tecnologia, PTDC/MAT/118682/2010,
Geometrias Riemannianas Especiais, 01/01/201231/12/2014 (research member) (responsible researcher: Rui Albuquerque. Funding: 12.000 Euros).
 Fundação
para a Ciencia e Tecnologia, PTDC/MAT/101007/2008,
Eigenvalues of the Laplacian: analytic, geometric and computational aspects
01/01/201031/12/2012
(research member) (responsible researcher: Pedro Freitas. Funding: 128.299 Euros).
 Fundação
para a Ciencia e Tecnologia, POCIPPCDT/MAT/60671/2004, Geometry of special
holonomy, 01/05/200530/04/2008 (responsible researcher: Isabel Salavessa.
Funding: 12.000 Euros).

Member of the European Project "Gadget" (Global Analysis and Differential Geometry,
European Team), in the framework of the UE programme "Human Capital and Mobility",
with the reference ERBCHRXCP920050, starting 1992.
Recent Collaborators

Juan J. Salamanca, Departamento de Matematicas, Universidad de Cordoba,
Spain.

Jing Mao,
Departamento de Matematica e Centro de Fisica das Interaccoes
Fundamentais, ISTUTL, Lisbon.

Ana Cristina C. Ferreira
Departamento de Matematica e Aplicacoes, Minho University, Braga.

Frank Morgan
Atwell Professor of Mathematics,
Department of Mathematics and Statistics.
Bronfman Science Center
Williams College
Williamstown, MA 01267, USA.

Pedro Freitas
Mathematical Physics GroupUL and Departement of Mathematics FMHUTL, Technical University of Lisbon.

Guanghan Li,
School of Mathematics and Computer Science,
Hubei University, Wuhan, 430062, People's Republic of China

Rui Albuquerque
Department of Mathematics, University of Evora

Ana Pereira do Vale
Department of Mathematics, University of Minho
Previous Collaborators

Giorgio Valli, University of Pavia, Italy

Duong Mihn Duc, Vietnam National University at Ho Chi Minh City, Vietnam

JeanPierre Ezin, Institut de Mathematiques et de Sciences Physiques,
PortoNovo, Republic of Benin

Marco Rigoli, University degli Studi di Milano, Italy

Armando Machado, Universidade de Lisboa
Experience as scientific adviser
 Jing Mao,
Eigenvalue Estimation and Some Results on Finite Topological Type,
Ph.D. thesis, Mathematics department of IST, 13 March 2013
(adviser: I.Salavessa, coadviser:
Pedro Freitas)

Dr. Guanghan Li, postdoc, during 20052006 (IST fellowship),
and during 20072008 (FCT fellowship SFRH/BPD/26554/2006),
at Instituto Superior Tecnico, Lisbon.

Ana Mafalda Alves Bagio Vaz de Araujo,
Minimal Surfaces, M.Sc. thesis, FCUL, January 1990.

Rui Pedro Lima Pinto Ribeiro de Albuquerque,
Curvatures of Leftinvariant SemiRiemannian Metrics on Lie Groups,
M.Sc. thesis FCUL, December 1996.
Member of Ph.D. exam committee
 Alma Luisa Albujer Brotons,
Geometria global de superficies espaciales en espacios producto lorentzianos,
Faculdad de Matematicas , Universidad Murcia, Murcia, Spain, 19 November 2008.
 Nuno Miguel Ferreira Correia,
Aplicacoes Harmonicas de Superficies de Riemann sobre Espacos Simetricos,
Universidade da Beira Interior, Covilha,
7 March 2012.
Other professional activities
reviewer of

Mathematical Reviews of the American Mathematical Society

Zentralblatt Math
referee for the:

Journal of Differential Equations,

Mathematische Nachrichten,

Bulletin of the London Mathematical Society,

Communications in Partial Differential Equations,

Frontiers of Mathematics in China,

Journal of Geometric Analysis,

Journal of Geometry and Physics

Journal of Inequalities and Applications,

Mathematical Proceedings of the Cambridge Philosophical Society

Pacifc Journal of Mathematics

Portugaliae Mathematica,

Proceedings Mathematical Sciences,

Publicaciones de la Real Sociedad Matematica Espanola,

Southeast Asian Bulletin of Mathematics
Prize and awards received
 Postdoc fellowship JNICT 1991
 Ph.D. fellowship Calouste Gulbenkian Foundation September 1995 August 1997
 Silver Medal 1988 of L'Association des Amis de Robert Schuman.
Other Interests
Ricardo Rupp Salavessa plays Bach, Bartok, Bazzini, Beethoven, Bruch, Copland, Mendelssohn, Paganini, Prokofiev, Sarasate, Schubert, Schumann, Tchaikovsky,
Vivaldi, Wieniawski, etc...
Youtube playlist
Additional Informations