Recent Submissions

  • The Peebles–Vilenkin quintessential inflation model revisited 

    Haro Cases, Jaume; Amorós Torrent, Jaume; Pan, Supriya (springer-Verlag, 2019-06-01)
    Article
    Open Access
    We review the well-known Peebles–Vilenkin (PV) quintessential inflation model and discuss its possible improvements in agreement with the recent observations. The improved PV model depends only on two parameters: the ...
  • Stable s-minimal cones in R 3 are flat for s ~ 1 

    Cabré Vilagut, Xavier; Cinti, Eleonora; Serra, Joaquim (2019-01-01)
    Article
    Restricted access - publisher's policy
    We prove that half spaces are the only stable nonlocal s-minimal cones in R3, for s¿(0,1) sufficiently close to 1. This is the first classification result of stable s-minimal cones in dimension higher than two. Its proof ...
  • A gradient estimate for nonlocal minimal graphs 

    Cabré Vilagut, Xavier; Cozzi, Matteo (2019-04-01)
    Article
    Restricted access - publisher's policy
    We consider the class of measurable functions defined in all of Rn that give rise to a nonlocal minimal graph over a ball of Rn. We establish that the gradient of any such function is bounded in the interior of the ball ...
  • Stability implies constancy for fully autonomous reaction-diffusion-equations on finite metric graphs 

    Von Below, Joachim; Lubary Martínez, José Antonio (2018-12-01)
    Article
    Open Access
    We show that there are no stable stationary nonconstant solutions of the evolution problem (1) for fully autonomous reaction-diffusion-equations on the edges of a finite metric graph G under continuity and Kirchhoff flow ...
  • Different reheating mechanisms in quintessence inflation 

    Haro Cases, Jaume (American Physical Society (APS), 2019-02-11)
    Article
    Open Access
    Different well-known ways to reheat the Universe, such as instant preheating, the creation of particles nearly or conformally coupled with gravity, or from the decay of products of a curvaton field, are revisited and ...
  • Bouncing cosmologies via modified gravity in the ADM formalism: Application to loop quantum cosmology 

    Haro Cases, Jaume; Amorós Torrent, Jaume (American Physical Society (APS), 2018-03-15)
    Article
    Open Access
    We consider the Arnowitt-Deser-Misner formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond general relativity modifying the gravitational ...
  • Optimal scalar products in the Moore-Gibson-Thompson equation 

    Pellicer, Marta; Solà-Morales Rubió, Joan de (2019-03-01)
    Article
    Open Access
    We study the third order in time linear dissipative wave equation known as the Moore-Gibson-Thompson equation, that appears as the linearization of a the Jordan-Moore-Gibson-Thompson equation, an important model in nonlinear ...
  • Stable solutions to some elliptic problems: minimal cones, the Allen-Cahn equation, and blow-up solutions 

    Cabré Vilagut, Xavier; Poggesi, Giorgio (2018-01-01)
    Article
    Restricted access - publisher's policy
    These notes record the lectures for the CIME Summer Course taught by the first author in Cetraro during the week of June 19–23, 2017. The notes contain the proofs of several results on the classification of stable solutions ...
  • Qualitative study in loop quantum cosmology 

    Aresté Saló, Llibert; Amorós Torrent, Jaume; Haro Cases, Jaume (2017-12-07)
    Article
    Restricted access - publisher's policy
    This work contains a detailed qualitative analysis, in general relativity and in loop quantum cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics ...
  • Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay 

    Cabré Vilagut, Xavier; Fall, Mouhamed Moustapha; Solà-Morales Rubió, Joan de (2018-12-01)
    Article
    Restricted access - publisher's policy
    We are concerned with hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are ...
  • Reheating in quintessential inflation via gravitational production of heavy massive particles: a detailed analysis 

    Haro Cases, Jaume; Yang, Weiqiang; Pan, Supriya (2019-01-01)
    Article
    Open Access
    An improved version of the well-known Peebles-Vilenkin model unifying early inflationary era to current cosmic acceleration, is introduced in order to match with the theoretical values of the spectral quantities provided ...
  • Preface of Llavefest: A broad perspective on finite and infinite dimensional dynamical systems 

    Cabré Vilagut, Xavier; Delshams Valdés, Amadeu; Gidea, Marian; Zeng, Chongchun (American Institute of Mathematical Sciences, 2018-12-01)
    Article
    Restricted access - publisher's policy
    We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete ...

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