Related papers: On weakly m-convex sets
Motivated by M-theory compactifications, we investigate optical properties of black holes in the Starobinsky-Bel-Robinsion gravity. Precisely, we study the shadows and the deflection angle of light rays by non-rotating and rotating black…
For a minimal submanifold of the Euclidean space, we prove monotonicity formulas for its (weighted) volume within images of concentric balls under M\"obius transformations.
After discussing some subtle issues concerning the computation of deflection angle, a general but simple expression of bending angle of light rays in weak deflection limit has been presented for a general static and spherically symmetric…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…
We discover new monotonicity formulae for minimal submanifolds in space forms, which imply the sharp area bound for minimal submanifolds through a prescribed point in a geodesic ball. These monotonicity formulae involve an energy-like…
Primal and dual algorithms are developed for solving the $n$-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers $m$ given Euclidean balls, each with a given center and radius. Each algorithm…
In this paper, we investigate the optical properties of a charged black hole in Einstein-Maxwell-scalar (EMS) theory. We evaluate the shadow cast by the black hole and obtain analytical solutions for both the radius of the photon sphere and…
Complete hyperbolicity of small Euclidean balls with respect to a C^1-smooth almost complex structure standard at origin is improved to give a complete hyperbolicity of strictly pseudoconvex domains. More precise (and lower) regularity…
This thesis consists of five papers about reduced spherical convex bodies and in particular spherical bodies of constant width on the $d$-dimensional sphere $S^d$. In paper I we present some facts describing the shape of reduced bodies of…
Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few…
This paper is devoted to the study of the $m$-point homogeneity property for the vertex sets of polytopes in Euclidean spaces. In particular, we present the classifications of $2$-point and $3$-point homogeneous polyhedra in $\mathbb{R}^3$.
We analyze the possibility of detecting, with optical methods, particle and photon trajectories predicted by general relativity for a weak spherically-symmetric gravitational field. We discuss the required sensitivities and the possibility…
Weak gravitational lensing of background galaxies offers an excellent opportunity to study the intervening distribution of matter. While much attention to date has focused on the two-point function of the cosmic shear, the three-point…
We describe a general method to obtain weak subconvexity bounds for many classes of $L$-functions. This has applications to a conjecture of Rudnick and Sarnak for the mass equidistribution of Hecke eigenforms (see arxiv.org:math/0809.1636).
In a Riemannian manifold, it is well known that the scalar curvature at a point can be recovered from the volumes (areas) of small geodesic balls (spheres). We show the scalar curvature is likewise determined by the relative capacities of…
In this talk I review some of the key questions that weak lensing observations of clusters can potentially answer, and sketch the progress that has been made to date in extracting quantitative estimates of masses and density profiles. A…
We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
We study weak gravitational lensing around a compact object with arbitrary quadrupole moment in the presence of plasma. The studied compact objects are considered to be spherically symmetric. The additional parameter $\epsilon$ regulating…
We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach…