相关论文: Starshapedeness for fully-nonlinear equations in C…
We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restrict ourselves to starshaped rings in a warped product of an…
We discuss the equation of state for cold, dense quark matter in perturbation theory, and how it might match onto that of hadronic matter. Certain choices of the renormalization scale correspond to a strongly first order chiral transition,…
We present a higher-categorical generalization of the "Karoubi envelope" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is the closure for absolute limits. Our…
We examine the geometry of the level sets of particular horizontally $p$-harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the level sets of the $p$-capacitary potential of a bounded…
We give a construction of direct limits in the category of complete metric scalable groups and provide sufficient conditions for the limit to be an infinite-dimensional Carnot group. We also prove a Rademacher-type theorem for such limits.
We give a new criterion for solvability of group equations, providing proofs of various generalizations of the Kervaire-Laudenbach conjecture for Connes-embeddable groups.
A Carnot group is polarizable if it carries a homogeneous norm whose powers are fundamental solutions for the $p$-sub-Laplacian operators for all $1<p \le \infty$. Such groups also support a system of horizontal polar coordinates. We prove…
In this paper, we present the geometric Hardy inequalities on the starshaped sets in the Carnot groups. Also, we obtain the geometric Hardy inequalities on half-spaces for general vector fields.
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of differential equations. Effective new techniques…
The structure of a star composed of locally non-electroneutral incompressible three-component matter is considered within the framework of general relativity. For thermodynamic quantities like the pressure, the solution can be represented…
We propose a new numerical method to calculate irrotational binary systems composed of compressible gaseous stars in Newtonian gravity. Assuming irrotationality, i.e. vanishing of the vorticity vector everywhere in the star in the inertial…
We introduce polystar bodies: compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection bodies. We prove that polystar bodies are uniformly dense in…
In this note, we prove the existence of one particular class of starshaped compact hypersurfaces, by deriving global curvature estimates for such hypersurfaces; this generalizes the main result in [Hypersurfaces of prescribed mixed…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.
In this work we present some new results obtained in a study of the phase diagram of charged compact boson stars in a theory involving a complex scalar field with a conical potential coupled to a U(1) gauge field and gravity. We here obtain…
Recent advances in nuclear theory combined with new astrophysical observations have led to the need for specific theoretical models that actually apply to phenomena on dense-matter physics. At the same time, quantum chromodynamics (QCD)…
Based on a closed formula for a star product of Wick type on $\CP^n$, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star-algebra (with coefficients contained in the…
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give…
We develop the formalism for determining the quasinormal modes of general relativistic multi-fluid compact stars in such a way that the impact of superfluid gap data can be assessed. Our results represent the first attempt to study true…