Isabel Salavessa ([email protected])

(+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

• Principal Investigator of the University of Lisbon / Technical University of Lisbon, since September 1997.
• Working at Center of Physics and Engineering of Advanced Materials (CeFEMA), at the Instituto Superior Técnico. since January of 2015.

Previous Positions

• Principal Investigator of Technical University of Lisbon working at Centro de Física das Interacções Fundamentais, at the Instituto Superior Técnico. 1997-2014.
• Assistant Researcher of the Technical University of Lisbon, 1992-1997.
• Assistant Researcher of the Instituto Nacional de Investigação Científica, Lisbon, 1991-1992.
• Visiting Researcher at the University of Maryland at College Park, 1991.
• Research Assistant of the Instituto Nacional de Investigação Científica, Lisbon, 1988-1991.
• Teaching Assistant of the University of Lisbon, 1985-1988.
• Junior Teaching Assistant of the University of Lisbon, 1983-1985.

Main Research Interests

• DIFFERENTIAL GEOMETRY AND GEOMETRIC ANALYSIS.
• Submanifolds with parallel mean curvature.
• Isoperimetric inequalities and spectral geometric theory.
• Bernstein-Heinz-Chern results for submanifolds with parallel mean curvature.
• Submanifolds in Calibrated Geometry.
• Submanifolds of pseudo-Riemannian 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, 53, Issue 2, (March 2018), 265-281.DOI:https://doi.org/10.1007/s10455-017-9577-x 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, 700-723. 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, 1376-1389 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 3-4, pp 701-724; DOI: 10.1007/s00526-013-0692-7
• The isoperimetric problem in higher codimension (with Frank Morgan) Manuscripta Mathematica, 142 (no.3-4)(2013) 369-382; DOI: 10.1007/s00229-012-0604-8 [arxiv:1203.3304]
• Stable 3-spheres in C^3. J. Mathematics Research, 4 , no.2 (April) 2012, 34-44; 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), 495-530. [arxiv:0911.4689]
• A spectral Bernstein theorem, (with Pedro Freitas), Ann. Mat. Pura ed Appl., 190(1)(2011),77-90, DOI: 10.1007/s10231-010-0139-0
• Bernstein-Heinz-Chern results in calibrated manifolds, (with G. Li), Rev. Mat. Iberoam., 26(2), 2010, 651-692 [arxiv:0802.0946]
• Mean Curvature Flow of Spacelike Graphs, (with G. Li), Math. Zeitschrift, 269(3-4) (2011), 697-719, DOI: 10.1007/s00209-010-0768-4. [arxiv:0804.0783]
• Graphic Bernstein Results in Curved Pseudo-Riemannian Manifolds, ( with G. Li), Journal of Geometry and Physics 59 (9)(2009) 1306-1313. DOI:10.1016/j.geomphys.2009.06.011).
• The G2-sphere of a 4-manifold, (with R. Albuquerque), Monatsh. Math., 158, No.4 (2009), 335-348. DOI 10.1007/s00605-008-0053-3.
• Erratum to: The G2-sphere of a 4-manifold, (with R. Albuquerque), Monatsh. Math., 160, No.1 (2010), 109-110. DOI 10.1007/s00605-010-0191-2.
• Forced convex mean curvature flow in Euclidean space, (with G. Li), Manuscripta Math. 126 (2008), 333-351. DOI 10.1007/s00229-008-0181-z.
• Spacelike graphs with parallel mean curvature, Bull. Belgian Math. Soc. Simon Stevin 15 (1)(2008), 65-76
• On the twistor space of pseudo-spheres, (with R. Albuquerque), Differential Geometry and its Applications 25 (2)(2007), 207-219
• Transgression forms in dimension 4, (with A. Pereira do Vale), Int. J. Geom. Meth. Mod. Phys. 3 no. 5-6 (2006) 1221-1254.
• Space-time formulation for curvature flow of high codimension (with G. Li), JP Journal of Geometry and Topology 6 no. (2006)303-318.
• On the Kähler angles of submanifolds Port. Math. (N.S.) (60) no.2 (2003), 215-235.
• Minimal submanifolds of Kähler-Einstein manifolds with equal Kähler angles, (with G. Valli), Pacific J.Math. 205 no.2 (2002), 197-235.
• Broadly-pluriminimal submanifolds of Kähler-Einstein manifolds, (with G. Valli), Yokohama Math.J., (48) (2001), no.2, 181-199.
• On a class of graphs with prescribed mean curvature, (with D.M. Duc), Manuscripta Math. 82 (1994) 227-234.
• Willmore submanifolds of the Möbius space and a Bernstein-type theorem, (with M. Rigoli), Manuscripta Math. 81 (1993) 203-222.
• Spherical-type hypersurfaces in a Riemannian manifold, (with J-P. Ezin and M. Rigoli), Israel J. Math. 71 (1990)(2), 193-209.
• Graphs with parallel mean curvature, Proc. Amer. Math. Soc. 107 (1989) 449-458.
• Conformal and isometric immersions of Riemannian manifolds, (with M.Rigoli) Math. Zeitschrift 196 (1987), no.2, 293--300.
• Grassmannian manifolds as subsets of Euclidean spaces, (with A. Machado), Differential geometry (Santiago de Compostela, 1984), 85-102, Res. Notes in Math.,131, Pitman, Boston, MA, 1985.

Selected Talks Published in Proceedings

• Mean Curvature Flow and Bernstein-Calabi Results for Spacelike Graphs, (with G. Li), VIII International Colloquium on Differential Geometry, Santiago de Compostela, Spain, 7-11 July 2008, satellite event of the 5th European Congress of Mathematics, Lopez, Jesus A. Alvarez(Ed), Garcia-Rio, Eduardo(Ed),World Scientific Publishing Company, April 2009, pp. 164-174, arxiv:0810.3371
• Mininal Submanifolds of Kähler-Einstein 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, 3-7 September 1999. http://www.emis.de/proceedings/Coimbra99/index.html

Selected Invited Talks (not published)

• Cheng’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, 10-13 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 17-18, 2004.
• Minimal Submanifolds of Kähler-Einstein Manifolds , invited talk at Special Session on Ricci Curvature and Related Topics, 966th AMS Meeting, Stevens Institute of Technology, Hoboken, NJ, USA, April 28-29, 2001.

Research Projects

• Fundação para a Ciencia e Tecnologia, PTDC/MAT/118682/2010, Geometrias Riemannianas Especiais, 01/01/2012-31/12/2014 (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 01/01/2010-31/12/2012 (research member) (responsible researcher: Pedro Freitas. Funding: 128.299 Euros).
• Fundação para a Ciencia e Tecnologia, POCI-PPCDT/MAT/60671/2004, Geometry of special holonomy, 01/05/2005-30/04/2008 (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 ERBCHRX-CP92-0050, 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, IST-UTL, 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 Group-UL and Departement of Mathematics FMH-UTL, 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
• Jean-Pierre Ezin, Institut de Mathematiques et de Sciences Physiques, Porto-Novo, 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, co-adviser: Pedro Freitas)
• Dr. Guanghan Li, postdoc, during 2005-2006 (IST fellowship), and during 2007-2008 (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 Left-invariant Semi-Riemannian 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

• Mathematical Reviews of the American Mathematical Society
• Zentralblatt Math

• 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