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The Peebles–Vilenkin quintessential inflation model revisited
(springerVerlag, 20190601)
Article
Open AccessWe review the wellknown 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 sminimal cones in R 3 are flat for s ~ 1
(20190101)
Article
Restricted access  publisher's policyWe prove that half spaces are the only stable nonlocal sminimal cones in R3, for s¿(0,1) sufficiently close to 1. This is the first classification result of stable sminimal cones in dimension higher than two. Its proof ... 
A gradient estimate for nonlocal minimal graphs
(20190401)
Article
Restricted access  publisher's policyWe 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 reactiondiffusionequations on finite metric graphs
(20181201)
Article
Open AccessWe show that there are no stable stationary nonconstant solutions of the evolution problem (1) for fully autonomous reactiondiffusionequations on the edges of a finite metric graph G under continuity and Kirchhoff flow ... 
Different reheating mechanisms in quintessence inflation
(American Physical Society (APS), 20190211)
Article
Open AccessDifferent wellknown 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
(American Physical Society (APS), 20180315)
Article
Open AccessWe consider the ArnowittDeserMisner 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 MooreGibsonThompson equation
(20190301)
Article
Open AccessWe study the third order in time linear dissipative wave equation known as the MooreGibsonThompson equation, that appears as the linearization of a the JordanMooreGibsonThompson equation, an important model in nonlinear ... 
Stable solutions to some elliptic problems: minimal cones, the AllenCahn equation, and blowup solutions
(20180101)
Article
Restricted access  publisher's policyThese 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
(20171207)
Article
Restricted access  publisher's policyThis 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
(20181201)
Article
Restricted access  publisher's policyWe 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
(20190101)
Article
Open AccessAn improved version of the wellknown PeeblesVilenkin 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
(American Institute of Mathematical Sciences, 20181201)
Article
Restricted access  publisher's policyWe prove that for any nontrivial 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 ...