Related papers: The Minkowski problem for the torsional rigidity

Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…

The Ehrhard-Borell inequality is a far-reaching refinement of the classical Brunn-Minkowski inequality that captures the sharp convexity and isoperimetric properties of Gaussian measures. Unlike in the classical Brunn-Minkowski theory, the…

We consider a class of one--dimensional non--convex non--coercive problems in the Calculus of Variations. We prove an existence result for this class of problems using a Liapunov type theorem on the range of non--atomic measures.

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is…

We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion…

We prove existence of multiple radial solutions to the Dirichlet problem for nonlinear equations involving the mean curvature operator in Lorentz-Minkowski space and a nonlinear term of concave-convex type. Solutions are found using…

An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over spherical caps, and the support function of the resulting…

The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of…

We consider a stress-energy tensor describing a pure radiation viscous fluid with conformal symmetry introduced in arXiv:1708.06255. We show that the corresponding equations of motions are causal in Minkowski background and also when…

We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson…

In this paper, we deal with the torsion log-Minkowski problem without symmetry assumptions via an approximation argument.

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant…

We prove the validity of the $p$-Brunn-Minkowski inequality for the intrinsic volume $V_k$, $k=2,\dots, n-1$, of convex bodies in $\mathbb{R}^n$, in a neighborhood of the unit ball, for $0\le p<1$. We also prove that this inequality does…

We consider a class of variational equations with exponential nonlinearities on a compact Riemannian surface, describing the mean field equation of the equilibrium turbulance with arbitrarily signed vortices. For the first time, we consider…

We present an abstract form of the Pr\'ekopa-Leindler inequality that includes several known -and a few new- related functional inequalities on Euclidean spaces. The method of proof and also the formulation of the new inequalities are based…

This paper explores the stability of Minkowski-type inequalities for hypersurfaces in warped product spaces. We establish a stability estimate that bounds the norm of the traceless second fundamental form of the hypersurface in terms of the…

In this paper, we consider a class of Hessian equations associated to the $L_p$-dual Christoffel-Minkowski problem for the case $p\geq q$. By combining the tools of constant rank theorem, the a priori estimates and the continuity method, we…

In this work we prove a Brunn-Minkowski-type inequality in the context of symplectic geometry and discuss some of its applications.

We study a class of nonlinear elliptic problems driven by a double-phase operator with variable exponents, arising in the modeling of heterogeneous materials undergoing phase transitions. The associated Poisson problem features a…