I'm a Principal Investigator of Reitoria da Universidade de Lisboa, and presently I work at Instituto Superior Técnico as a member of Grupo de Física Matemática (IST), at Pavilhão da Física IST, 1-1.1 (shared office with George Rupp), Av. Rovisco Pais, 1049-001 Lisboa, Portugal. Telephone: 218419105, email: isabel.salavessa@tecnico.ulisboa.pt I made my Ph.D. with Professor James Eells in 1987 at the University of Warwick, UK, supported by a fellowship from Calouste Gulbenkian Foundation, Lisbon, and made a post-doc at Maryland University, USA, with support of a JNICT fellowship. During my PhD I spent one year (1986) at ICTP-International Centre for Theoretical Physics, Triste, Italy. I work within Riemannian and pseudo-Riemannian Geometry and Geometric Analisys, namely submanifolds with constant mean curvature, isoperimetric inequalities and rigidity results, using maximum principles of PDE or evolution equations (mean curvature flow). Recently I've been working mainly in Spectral Geometry; in particular on Pólya's conjecture for non-tiling domains of euclidean or spherical submanifolds. I've been reviewer for the Mathematical Reviews of the American Mathematical Society, and the Zentralblatt Math, and a referee for 15 international mathematical journals. Most relevant works 1. Graphs with parallel mean curvature. Proceedings of the American Mathematical Society 107 (2) (1989), 449-449. 10.2307/2047835. (62 citations (Google source)) 2. Graphic Bernstein results in curved pseudo-Riemannian manifolds, (with G. Li). Journal of Geometry and Physics 59 (9) (2009), 1306-1313. 10.1016/j.geomphys.2009.06.011 (22 citations) 3. Mean curvature flow of spacelike graphs, (with G. Li). Mathematische Zeitschrift 269, 3-4 (2011), 697-719. 10.1007/s00209-010-0768-4. (27 citations) 4. The isoperimetric problem in higher codimension, (with F. Morgan). Manuscripta Mathematica 142 (3-4) (2013): 369-382. 10.1007/s00229-012-0604-8. 5. Spherical symerization and the first eigenvalue of geodesic disks on manifolds, (with P. Freitas and J. Mao). Calculus of Variations and Partial Differential Equations, 51 (2014), 701-724. 10.1007/s00526-013-0692-7. (28 citations) 6. Families of non-tiling domains satisfying Pólya's conjecture (with P. Freitas). Journal of Mathematical Physics 64, 121503 (2023) https://doi.org/10.1063/5.0161050 https://arxiv.org/abs/2204.08902 abstract: We show the existence of classes of non-tiling domains satisfying Pólya's conjecture in any dimension, in both the Euclidean and non-Euclidean cases. This is a consequence of a more general observation asserting that if a domain satisfies Pólya's conjecture eventually, that is, for a sufficiently large order of the eigenvalues, and may be partitioned into p non-overlapping isometric sub-domains, with p arbitrarily large, then there exists an order p0 such that for p larger than p0 all such sub-domains satisfy Pólya's conjecture. In particular, this allows us to show that families of sectors of domains of revolution with analytic boundary, and thin cylinders satisfy Pólya's conjecture, for instance. We also improve upon the Li-Yau constant for general cylinders in the Dirichlet case. citations: (a)Maximization of Neumann Eigenvalues, D. Bucur, E. Martinet, E. Oudet, Archive for Rational Mechanics and Analysis, volume 247 (19), (2023). (b) Pólya's conjecture for Euclidean balls, N. Filonov, M. Levitin, I. Polterovich, D.A. Sher, Inventiones Mathematicae, Volume 234, p. 129–169, (2023). (c) Semiclassical estimates for eigenvalue means of Laplacians on spheres, D. Buoso, P. Luzzini, L. Provenzano, J. Stubbe. Journal of Geometric Analysis, Volume 33, article number 280, (2023) previous homepage http://cfif.ist.utl.pt/~isabel/