1,260 research outputs found
Quantized fields and gravitational particle creation in f(R) expanding universes
The problem of cosmological particle creation for a spatially flat,
homogeneous and isotropic Universes is discussed in the context of f(R)
theories of gravity. Different from cosmological models based on general
relativity theory, it is found that a conformal invariant metric does not
forbid the creation of massless particles during the early stages (radiation
era) of the Universe.Comment: 14 pages, 2 figure
Generic dynamics of 4-dimensional C2 Hamiltonian systems
We study the dynamical behaviour of Hamiltonian flows defined on
4-dimensional compact symplectic manifolds. We find the existence of a
C2-residual set of Hamiltonians for which every regular energy surface is
either Anosov or it is in the closure of energy surfaces with zero Lyapunov
exponents a.e. This is in the spirit of the Bochi-Mane dichotomy for
area-preserving diffeomorphisms on compact surfaces and its continuous-time
version for 3-dimensional volume-preserving flows
Weighted Orlicz regularity for fully nonlinear elliptic equations with oblique derivative at the boundary via asymptotic operators
We prove weighted Orlicz-Sobolev regularity for fully nonlinear elliptic
equations with oblique boundary condition under asymptotic conditions of the
following problem: in the bounded domain () and on ,
under suitable assumptions on the source term , data and
. Our approach guarantees such estimates under conditions where the
governing operator does not require a convex (or concave) structure. We
also deal with weighted Orlicz-type estimates for the obstacle problem with
oblique derivative condition on the boundary. As a final application, the
developed methods provide weighted Orlicz-BMO regularity for the Hessian,
provided that the source lies in that space and in weighted Orlicz space
associated.Comment: 27 pages. arXiv admin note: substantial text overlap with
arXiv:2302.0917
The mean curvature of cylindrically bounded submanifolds
We give an estimate of the mean curvature of a complete submanifold lying
inside a closed cylinder in a product Riemannian manifold
. It follows that a complete hypersurface of given
constant mean curvature lying inside a closed circular cylinder in Euclidean
space cannot be proper if the circular base is of sufficiently small radius. In
particular, any possible counterexample to a conjecture of Calabion complete
minimal hypersurfaces cannot be proper. As another application of our method,
we derive a result about the stochastic incompleteness of submanifolds with
sufficiently small mean curvature.Comment: First version (December 2008). Final version, including new title
(February 2009). To appear in Mathematische Annale
Eigenvalue estimates for submanifolds of warped product spaces
We give lower bounds for the fundamental tone of open sets in minimal
submanifolds immersed into warped product spaces of type ,
where . We also study the essential spectrum of these
minimal submanifolds.Comment: 17 page
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