Isabel Salavessa (isabel.salavessa@ist.utl.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: Prof. James Eells (Warwick), exam committee: Prof. Nigel Hitchin, MA, DPhil (Oxford) and Prof. David Epstein, FRS (Warwick).

Present Position

• Principal Investigator of the Technical University of Lisbon, since September 1997.
• Working at Centro de Física das Interacções Fundamentais, at the Instituto Superior Técnico.

Previous Positions

• 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.
• Geometric flows.
• Willmore submanifolds.

Selected Papers and Preprints

• The Isoperimetric Problem in HIgher Codimension (with Frank Morgan) [arxiv:1203.3304]
• Stable 3-spheres in C^3. To apper in J. Mathematics Research 4 , no.2 (April) 2012 [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
• On the spectrum of X-bounded minimal submanifolds , http://arxiv.org/abs/0901.1246
• 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 Vol 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.
• Transgression forms in dimension 4, (with A. Pereira do Vale), Int.J. Geom. Meth. Mod. Phys. 3 no. 5-6 (2006) 1221-1254.
• Minimal submanifolds of Kähler-Einstein manifolds with equal Kähler angles, (with G. Valli), Pacific J.Math. 205 no.2 (2002), 197-235.
• On a class of graphs with prescribed mean curvature, (with D.M. Duc), Manuscripta Math. 82 (1994) 227-234.
• 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

• 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.
• 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
• 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.
• 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

Projects

• 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).
• 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, PTDC/MAT/118682/2010, Geometrias Riemannianas Especiais, 01/10/2011-30/09/2014 (research member) (responsible researcher: Rui Albuquerque. Funding: 12.000 Euros).

Recent Collaborators

• 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

PhD Students

• Jing Mao, PhD program of Mathematics department of IST (supervised by myself and by Pedro Freitas)

Prize

Silver Medal 1988 of L'Association des Amis de Robert Schuman.

Additional Informations

Additional Informations

David Russell Violin Masterclass 2010 in Lisbon (1), (2), (3), (4), (Ravel's Tzigane)

Ricardo Rupp Salavessa plays Mozart Violin Concerto no. 3 (KV216), 1st movement, 3rd. movement

Pierre Rode's Caprice no.7 (2010)

Kreisler's "Praeludium and Allegro" (2009)

Copland's "Hoedown", from Rodeo,