相关论文: The hessian in spin foam models

In this paper, we investigate a class of doubly nonlinear evolutions PDEs. We establish sharp regularity for the solutions in H\"older spaces. The proof is based on the geometric tangential method and intrinsic scaling technique. Our…

We study stochastic homogenization of a quasilinear parabolic PDE with nonlinear microscopic Robin conditions on a perforated domain. The focus of our work lies on the underlying geometry that does not allow standard homogenization…

We present regularity results for nonlinear drift-diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drift term with respect to previous results and additionally…

We present a method for constructing stationary, asymptotically flat, rotating solutions of Einstein's field equations. One of the spun-up solutions has quasilocal mass but no global mass. It has an ergosphere but no event horizon. The…

In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the other hand, Schatzman proved that in the vector case this…

The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical…

In this paper we complete the topological description of the space of representations of the fundamental group of a punctured surface in SL(2,R) with prescribed behavior at the punctures and nonzero Euler number, following the strategy…

In this paper we study classification of homogeneous solutions to the stationary Euler equation with locally finite energy. Written in the form $u = \nabla^\perp \Psi$, $\Psi(r,\theta) = r^{\lambda} \psi(\theta)$, for $\lambda >0$, we show…

A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $\gamma -$law…

In this paper, we consider the evolution of the Vortex Filament equation (VFE): \begin{equation*} \mathbf X_t = \mathbf Xs \wedge \mathbf Xss, \end{equation*} taking $M$-sided regular polygons with nonzero torsion as initial data. Using…

We show that $\mathfrak{aff}(n)$, the Lie algebra of affine transformations of ${\mathbb R}^n,$ is formally and analytically nondegenerate in the sense of A. Weinstein. This means that every analytic (resp., formal) Poisson structure…

We construct stationary flat three-dimensional Lorentzian manifolds with singularities that are obtained from Euclidean surfaces with cone singularities and closed one-forms on these surfaces. In the application to (2+1)-gravity, these…

In this paper, we present a problem involving fully nonlinear elliptic operators with Hamiltonian, which can present a singularity or degenerate as the gradient approaches the origin. The model studied here, allows the appearance of plateau…

Using numerical calculations, we compare three versions of the Barrett-Crane model of 4-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we show…

We investigate the regularity of the solutions for a class of degenerate/singular fully nonlinear nonlocal equations. In the degenerate scenario, we establish that there exists at least one viscosity solution of class $C_{loc}^{1, \alpha}$,…

In this work, we obtain a short time solution for a geometric flow on noncompact affine Riemannian manifolds. Using this result, we can construct a Hessian metric with nonnegative bounded Hessian sectional curvature on some Hessian…

We provide an algorithm to estimate the divergence degree of the Lorentzian EPRL-FK spin foam amplitudes for arbitrary 2-complexes. We focus on the "self-energy" and "vertex renormalization" diagrams and find an upper bound estimate. We…

We consider spin manifolds with an Einstein metric, either Riemannian or indefinite, for which there exists a Killing spinor. We describe the intrinsic geometry of nondegenerate hypersurfaces in terms of a PDE satisfied by a pair of induced…

A full theory for hinged beams and degenerate plates with multiple intermediate piers is developed. The analysis starts with the variational setting and the study of the linear stationary problem in one dimension. Well-posedness results are…

In this paper we prove Holder regularity of the derivative of radial solutions to fully nonlinear equations when the operator is hessian, homogenous of degree 1 in the Hessian, homogenous of some degree $\alpha>-1$ in the gradient and which…