Related papers: Curvature-Dimension for Autonomous Lagrangians
We examine universal curvature identities for pseudo-Riemannian manifolds with boundary. We determine the Euler-Lagrange equations associated to the Chern-Gauss-Bonnet formula and show that they are given solely in terms of curvature {and…
The Gaussian curvature of a two-dimensional Riemannian manifold is uniquely determined by the choice of the metric. The formulas for computing the curvature in terms of components of the metric, in isothermal coordinates, involve the…
We study the condition that the theory is unitary and stable in three-dimensional gravity with most general quadratic curvature, Lorentz-Chern-Simons and cosmological terms. We provide the complete classification of the unitary theories…
We consider the nonlinear eigenvalue problem, with Dirichlet boundary condition, for a class of very degenerate elliptic operators, with the aim to show that, at least for square type domains having fixed volume, the symmetry of the domain…
In this paper we establish new simple local geometric criteria for discrete entropic curvature introduced in [47] that are powerful enough to capture many geometric properties of complex models arising in mathematical physics. These results…
In this paper the dynamic compactification in Lovelock gravity with a cubic term is studied. The ansatz will be of space-time where the three dimensional space and the extra dimensions are constant curvature manifolds with independent scale…
We obtain new lower bounds for the first non-zero eigenvalue of the scalar sub-Laplacian for 3-Sasaki metrics, improving Lichnerowicz-Obata type estimates by Ivanov et al. The limiting eigenspace is fully decribed in terms of the…
In the near-horizon region, black holes exhibit an infinite-dimensional symmetry reminiscent of the Bondi-Metzner-Sachs (BMS) supertranslations. The conserved charges associated with this symmetry can be computed in gravitational theories…
The Lagrangian derivatives of finite-time Lyapunov exponents and the corresponding characteristic directions are shown to satisfy time-asymptotic differential constraints in chaotic flows. The constraints are valid for any metric tensor,…
In this paper we give pinching theorems for the first nonzero eigenvalue of the Laplacian on the compact hypersurfaces of ambient spaces with bounded sectional curvature. As application we deduce rigidity results for stable constant mean…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
In this article we study the stability problem for positive quaternion-K\"ahler manifolds. We give a description of infinitesimal Einstein deformations and destabilising directions in terms of Laplace eigenfunctions and a special class of…
We introduce several new notions of (sectional) curvature bounds for Lorentzian pre-length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study…
The role of curvature in relation with Lie algebra contractions of the pseudo-ortogonal algebras so(p,q) is fully described by considering some associated symmetrical homogeneous spaces of constant curvature within a Cayley-Klein framework.…
We prove rigidity for the Lichnerowicz-type eigenvalue estimate for the Kohn Laplacian on strictly pseudoconvex three-manifolds with nonnegative CR Paneitz operator and positive Webster curvature.
We work on a 4-manifold equipped with Lorentzian metric $g$ and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric $h$, the pullback of…
We explore holographic entanglement entropy for Minkowski spacetime in three and four dimensions. Under some general assumptions on the putative holographic dual, the entanglement entropy associated to a special class of subregions can be…
We argue that four-dimensional quantum gravity may be essentially renormalizable if one relaxes the assumption of metricity of the theory. We work with Plebanski formulation of general relativity in which the metric (tetrad), the…
We derive, in curved spacetime, the most general Lorentz-violating electromagnetic Lagrangian containing dimension-five operators with one more derivative than the Maxwell term in the hypothesis that Lorentz symmetry is broken by a…
By using a coupling method, an explicit log-Harnack inequality with local geometry quantities is established for (sub-Markovian) diffusion semigroups on a Riemannian manifold (possibly with boundary). This inequality as well as the…