Research Interests

  • Differential Geometry
  • Riemannian Geometry
  • Minimal Submainfolds
  • Controlled Mean Curvature Submanifolds
  • Geometry of Quantum States


  • G. P. Bessa, V. Gimeno, L. P. Jorge Dirichlet spectrum and Green function [arXiv:1605.04355]
  • J.C Garcia-Escartin, V. Gimeno, J. J. Moyano-Fernandez Multiple photon Hamiltonian in linear quantum optical networks [arXiv: 1605.02653]
  • P. Bessa, V. Gimeno and V. Palmer Asymptotically extrinsic tamed submanifolds [arXiv: 1512.08667]
  • V. Gimeno and V. Palmer Mean curvature, volume and properness of isometric immersions. To appear in TAMS [arXiv: 1504.00055]
  • V. Gimeno Large time behavior of the on-diagonal heat kernel for minimal submanifolds with polynomial volume growth. [arXiv: 1310.4643]

Published Papers

  • C. M. Brandao and V. Gimeno On the total curvature and extrinsic area growth of surfaces with tamed second fundamental form. Differential Geometry and its Applications. (2016) 45 [arXiv: 1412.4929]
  • V. Gimeno and I. Gozalbo Conformal type of ends of revolution in space forms of constant sectional curvature.Annals of Global Analysis and Geometry, (2) 49 (2016), 143-164. [arXiv: 1505.06834]
  • V. Gimeno, Isoperimetric inequalities for submanifolds. Jellett–Minkowski's formula revisited. Proc. Lond. Math. Soc. (3) 110 (2015), no. 3, 593–614. [ arXiv:1306.2478]
  • V. Gimeno and S. Markvorsen Ends, Fundamental Tones, and Capacities of Minimal Submanifolds Via Extrinsic Comparison Theory. Potential Anal. 42 (2015), no. 4, 749–774. [ arXiv:1401.1392]
  • V. Gimeno and V. Palmer Volume Growth, Number of Ends and the Topology of a Complete Submanifold. J. Geom. Anal. 24 (2014), no. 3, 1346–1367. [ 1112.4042]
  • V. Gimeno On the fundamental tone of minimal submanifolds with controlled extrinsic curvature. Potential Anal. 40 (2014), no. 3, 267–278. [arXiv: 1301.1148]
  • V. Gimeno and V. PalmerVolume growth of submanifolds and the Cheeger Isoperimetric Constant Proc. Amer. Math. Soc. 141 (2013), no. 10, 3639–3650.[arXiv: 1104.5625]
  • V. Gimeno and J.M. Sotoca Geometric approach to non-relativistic Quantum Dynamics of mixed states. J. Math. Phys. 54 (2013), no. 5, 052108, 12 pp. [arXiv: 1302.1333]
  • V. Gimeno and V. PalmerExtrinsic isoperimetry and compactification of minimal surfaces in Euclidean and Hyperbolic spaces. Israel J. Math. 194 (2013), no. 2, 539–553.[arXiv: 1011.5380]

In preparation

  • A lower bound for the area of a foam. With S. Markvorsen and J.M Sotoca.
  • Number of ends, Area growth and quantization of the extrinsic curvature for minimal surfaces in the hyperbolic space. With I. Gozalbo and V. Palmer.
  • Geometric aspects of the Schrodinger's equation on surfaces With S. Markvorsen
  • Upper Bounds for the Poincare Recurrence Time in Quantum Mixed States With J. Sotoca.
  • An approximation to the evolution of the Hamiltonian in linear quantum-optical networks. With J.C. Garcia-Escartin and J. J. Moyano-Fernandez