**Home Research Projects Collaborators Publications Selected Talks ****Supervision Exam committee**** **

**About myself**

I'm a Principal Investigator of Universidade de Lisboa, and presently I work at *Instituto Superior Técnico*as a member of Grupo de Física Matemática UL, at Pavilhão da Física IST, 1-1.1 (shared office with George Rupp), Av. Rovisco Pais, 1049-001 Lisboa, Portugal.

*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), and more recently I've been working mainly in **Spectral Geometry**.

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**

* Graphs with parallel mean curvature.* Proceedings of the American Mathematical Society 107 (2) (1989), 449-449. 10.2307/2047835. (59 citations (Google source))

* 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)

** Mean curvature flow of spacelike graphs,** (with

**G. Li**). Mathematische Zeitschrift 269, 3-4 (2011), 697-719. 10.1007/s00209-010-0768-4. (21 citations)

* The isoperimetric problem in higher codimension*, (with

**F. Morgan**). Manuscripta Mathematica 142 (3-4) (2013): 369-382. 10.1007/s00229-012-0604-8.

* 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. (25 citations)

* Families of non-tiling domains satisfying Pólya's conjecture *(with

**P. Freitas**). Preprint (2022), submited.

I was awarded with the Silver Medal of L'Association des Amis de Robert Schuman (1988).

###### homepage of* Grupo de Física Matemática UL *

previous homepage http://cfif.ist.utl.pt/~isabel/

*Grupo de Física Matemática UL*

**Participation in Research Projects**

Member of the ** European Project Gadget **(

*), in the framework of the UE programme Human Capital and Mobility, with the reference ERBCHRXCP920050, (1992-2002).*

**Global Analysis and Differential Geometry, European Team**PI in the FCT project POCIPPCDT/MAT/60671/2004, * Special Holonomy Geometry*, (1/5/2005-3/4/2008).

Research member of the original team in the FCT project PTDC/MAT/101007/2008. * Eigenvalues of the Laplacian: analytic, geometric and computational aspects,* (18/01/2010-17/05/2013), with Freitas as the PI.

Research member in the FCT project PTDC/MAT/118682/2010, * Geometrias Riemannianas Especiais*, (01/01/2012-30/12/2014), with Rui Albuquerque as PI.

**Collaborators**

I' have colaborated with the following Mathematicians:

**Pedro Freitas** (U.Lisboa) **Frank Morgan** (Williams College) **Jing Mao **(Hubei U.) **Ana Cristina Ferreira** (U.Minho) **Juan J. Salamanca** (U.Córdoba) **Rui Albuquerque** (U.Évora) **Ana Pereira do Vale** (U.Minho) **Giorgio Valli **(U.Pavia) **Guanghan Li** (Hubei U.) **Duong Minh Duc** (Ho-Chi-Minh City U.) **Marco Rigoli** (U.Milano) **Jean-Paul Ezin** (IMSP Porto-Novo, Benin)**Armando Machado** (U.Lisboa)

**Research articles in international journal and Preprints**

**28**- **Families of non-tiling domains satisfying Pólya's conjecture, **(with **P. Freitas**). Preprint (2022), submited.**27**- * Pólya type inequalities on spheres and hemispheres*, (with

**P. Freitas**and

**J. Mao**). Preprint (2021), submited.

**26**-

**Heinz mean curvature estimates in warped product spaces M × e f N**. Annals of Global Analysis and Geometry 53 (2018), 265-281. 10.1007/s10455-017-9577-x

**25**-

*(with*

**Dirichlet principal eigenvalue comparison theorems in geometry with torsion**,**A.C. Ferreira**). Journal of Mathematical Analysis and Applications 453 2 (2017), :700-723. 10.1016/j.jmaa.2017.04.030.

**24**-

**(with**

*Uniqueness of f-minimal hypersurfaces in warped product manifolds*,**J.J. Salamanca**). Journal of Mathematical Analysis and Applications 422 2 (2015): 1376-1389. 10.1016/j.jmaa.2014.09.028

**23**-

**Spherical symmetrization and the first eigenvalue of geodesic disks on manifolds,**(with

**P. Freitas**and

**J.Mao**). Calculus of Variations and Partial Differential Equations, 51 (3-4)(2014): 701-724. 10.1007/s00526-013-0692-7

**22**-

**The isoperimetric problem in higher codimension**(with

**F. Morgan**). Manuscripta Mathematica 142(3-4) (2013): 369-382. 10.1007/s00229-012-0604-8

**21**-

**Stable 3-spheres in C3**

**.**Journal of Mathematics Research 42 (2012):

http://www.ccsenet.org/journal/index.php/jmr/article/view/13403.

**20**-

**A spectral Bernstein theorem**, (with

**P. Freitas**). Annali di Matematica Pura ed Applicata 190 1 (2011), 77-90. 10.1007/s10231-010-0139-0

**19**-

**Mean curvature flow of spacelike graphs**(with

**G. Li**). Mathematische Zeitschrift 269 3-4 (2011): 697-719. 10.1007/s00209-010-0768-4

**18-**Erratum to:

**, (with**

*The G2 sphere of a 4-manifold***R. Albuquerque**) Monatshefte Math., (2009), 158, (335-348), 10.1007/s00605-008-0053-3). Monat. fur Mathematik 160 1 (2010): 109-110. 10.1007/s00605-010-0191-2

**17**-

*. Bulletin of the Brazilian Mathematical Society 41(4) (2010): 495-530. 10.1007/s00574-010-0023-y*

**Stability of submanifolds with parallel mean curvature in calibrated manifolds****16**-

*(with*

**Bernstein-Heinz-Chern results in calibrated manifolds,****G. Li)**, Revista Matematica Iberoamericana 26(2) (2010). 651-692. https://projecteuclid.org/euclid.rmi/1275671315

**15**-

*, (with*

**Graphic Bernstein results in curved pseudo-Riemannian manifolds****G. Li**). Journal of Geometry and Physics 59(9)(2009):1306-1313. 10.1016/j.geomphys.2009.06.011

**14-**

*, (with*

**The G2 sphere of a 4-manifold****R. Albuquerque**). Monatshefte fur Mathematik 158 4 (2009): 335-348. 10.1007/s00605-008-0053-3

**13**-

*(with*

**Forced convex mean curvature flow in Euclidean space,****G.Li**). Manuscripta Mathematica 126(3) (2008), 333-351. 10.1007/s00229-008-0181-z

**12**-

*. Bulletin of the Belgian Mathematical Society - Simon Stevin 15(1) (2008), 65-76. https://projecteuclid.org/euclid.bbms/1203692447.*

**Spacelike graphs with parallel mean curvature****11**-

**On the twistor space of pseudo-spheres**, (with

**R. Albuqurque**). Differential Geometry and its Application 25(2) (2007), 207-219. 10.1016/j.difgeo.2006.08.004

**10**-

*(with*

**Space-time formulation for curvature flow of high codimension.****G.Li**) JP Journal of Geometry and Topology 6 no.3 (2006), p.303-318 6(3) (2006). 303-318. http://www.pphmj.com/journals/jpgt.htm.

**9**-

**Transgression forms in dimension 4,**(with

**A. Pereira do Vale**). International Journal of Geometric Methods in Modern Physics 3 (5-6) (2006). 1221-1254 10.1142/s0219887806001442

**8-**

*Portugaliae Mathetmatica (N.S.) 60 (2) (2003), 215-235. https://www.emis.de/journals/PM/60f2/.*

**On the Kähler angles of submanifolds**.**7-**

**Minimal submanifolds of Kähler-Einstein manifolds with equal Kähler angles**, (with

**G. Valli**). Pacific Journal of Mathematics 205(1) (2002), 197-235. 10.2140/pjm.2002.205.197

**6**-

*, (with*

**Broadly-pluriminimal submanifolds of Kähler-Einstein manifolds****G. Valli**). Yokohama Math. J. 48 (2001), no. 2, 181?199.

**5**-

**(with**

*On a class of graphs with prescribed mean curvature*,**Dong Minh Duc**). Manuscripta Mathematica 82 1 (1994), 227-239.10.1007/BF02567699

**4**-

*(with*

**Willmore submanifolds of the Möbius space and a Bernstein-type theorem,****M. Rigoli**) Manuscripta Mathematica 81(1)(1993): 203-222. 10.1007/BF02567854

**3**-

*(with*

**Spherical-type hypersurfaces in a Riemannian manifold****J.-P. Ezin**, and

**M. Rigoli**); Israel Journal of Mathematics 71 (2) (1990): 193-209. 10.1007/BF02811884

**2**-

*Proceedings of the American Mathematical Society 107 (2) (1989), 449-449. 10.2307/2047835*

**Graphs with Parallel Mean Curvature**,**1**-

*(with*

**Conformal and isometric immersions of Riemannian manifolds**,**M. Rigoli**). Mathematische Zeitschrift 196(2) (1987), 293-300. 10.1007/BF01163662

**Thesis**

**Graphs with parallel mean curvature and a variational problem in Conformal Geometr**y*,*Ph.D thesis, University of Warwick, 1987.

**Communications published in proceedings**

**4**-** *** 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. 5164-174, arxiv:0810.3371

**3**-

*, (with*

**Residue Formulas for Minimal Submanifolds****A. Pereira do Vale**). Proc. XV Intern. Workshop on Geometry and Physics, Tenerife, Spain, Sept. 11-16, 2006. Publ. de la RSME 11 (2007), 353-358.

**2**-

**Minimal submanifolds of Kähler- Einstein manifolds without complex directions and of half dimension**, (with

**G. Valli**). Summer School on Differential Geometry (Coimbra, 1999). ed. 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

**1**-

**, (with**

*Grassmannian manifolds as subsets of Euclidean spaces***A.Machado**).Proc. 5th Int. Colloq., Santiago de Compostela, Spain, 1984, Research Notes in Mathematics, 131, 85-102, Pitman Adv. Pub. Prog., Boston-London-Melbourne (1985) https://arxiv.org/abs/2101.09731 http://www.ams.org/mathscinet-getitem?mr=864860.

**Selected Invited Talks **(not published)

**5**- * Cheng's type comparison results for the principal eigenvalue of a V -drift Laplacian on a Riemannian manifold* (with

**Ana C. Ferreira**). International Meeting AMS/EMS/SPM, 10-13, June, 2015, Porto, Special Session 22 (Geometric Analysis) p. 39. Program abstract

**4**-

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

**3**-

*, invited talk at Dep. Geometria e Topologia, Universidad de Granada, Spain, 3 April 2009.*

**The Spectrum of Minimal Submanifolds****2**-

**invited talk at Workshop: Submanifolds Sendai 2004, Tohoku University, Sendai Japan, February 17-18, 2004. (*)**

*Angles of Minimal Submanifolds*,**1**-

*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.*

**Minimal Submanifolds of Kähler-Einstein Manifolds,**###### (*) with Prof. Katsuei Kenmotsu, Tohoku University, 2004

**Supervision of Masters degree**

M.Sc of **Ana Mafalda Vaz de Araújo** (*Minimal Surfaces*, Dec. 1990) Universidade de Lisboa.

M.Sc** Rui Pedro L.P. Ribeiro de Albuquerque** (*Curvature of Left invariant Semi-Riemannian Lie groupes*, Dec. 1996), Universidade de Lisboa

**Supervision of PhD degree, posgraduate and post-doc**

Posdoc researcher** Guanghan Li**** **(2005-2006) (IST fellowship) and (2007- 2008) Instituto Superior Técnico. (FCT fellowship SFRH/BPD/26554/2006).

(with **Pedro Freitas**) **Jing Mao**, who had a scholarship from FCT (SFRH/BD/60313/2009), as Ph.D. student in Mathematics at Instituto Superior Técnico, Lisbon (*Eigenvalue Estimation and Some Results on Finite Topological Type*) (2010-2013).

* Juan J. Salamanca*, Ph.D. student of Prof. Alfonso Romero, University of Granada, IST (3 months) in 2014.

(with **P. Freitas**) posdoc **Jing Mao**, Instituto Superior Técnico, 2018 with a grant from the Chinese Scholarship Council.

**Member of exam committee**

Member of the Ph.D. exam committee of **Alma Luisa Albujer Brotons**, *Geometria global de superficies espaciales en espacios producto lorentziano*, Faculdad de Matematicas, Universidad Murcia, Spain (November 2008, student of Prof. L. Alias).

Member of the Ph.D. exam committee of **Nuno Miguel Ferreira Correia***,* *Aplicações Harmónicas de Superfícies de Riemann sobre Espaços Simétricos* Universidade da Beira Interior, Covilhã (2012, student of Prof. R. Pacheco).

External Referee Report of Ph.D. thesis of *Daniel de la Fuente Benito,**Some problems on prescribed mean curvature and Kinematics in General Relativity*, Universidad de Granada, Spain (2016, student of Prof. A. Romero).