Related papers: Rigidity theorems by the logarithmic capacity
We explain the need for a theory of quantum gravity and some general ideas about string theory, including the idea of the derivation of the Hawking Bekenstein entropy formula for extremal black holes. We then give a general description of…
We prove precise conditional estimates for the third moment of the logarithm of the Riemann zeta function, refining what is implied by the Selberg central limit theorem, both for the real and imaginary parts. These estimates match…
It is proved that for any domain in $\mathbb C^n$ the Caratheodory--Eisenman volume is comparable with the volume of the indicatrix of the Caratheodory metric up to small/large constants depending only on $n.$ Then the "multidimensional…
In this expository article, we summarize what is known about maximum likelihood thresholds of Gaussian models, paying special attention to connections with rigidity theory.
The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension $\geq 3$. Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity…
We deal with the rigidity conjecture of symbolic powers over regular rings. This was asked by Huneke. Along with our investigation, we confirm a conjecture [7, Conjecture 3.8].
We study the connection between weighted Bergman kernel and Green's function on a domain W lying in C for which the Green's function exists.
In this letter, we consider the theory of $F(R)$ gravity with the lagrangian density $ \pounds = R+\alpha R^2 + \beta R^2 \ln \beta R $. We obtain the constant curvature solutions and find the scalar potential of the gravitational field. We…
We discuss the possibility of a class of gauge theories, in four Euclidean dimensions, to describe gravity at quantum level. The requirement is that, at low energies, these theories can be identified with gravity as a geometrodynamical…
Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner's symmetral…
The Newtonian limit of fourth-order gravity is worked out discussing its viability with respect to the standard results of General Relativity. We investigate the limit in the metric approach which, with respect to the Palatini formulation,…
We study the curvature condition which uniquely characterizes the hemisphere. In particular, we prove the Min-Oo conjecture for hypersurfaces in Euclidean space and hyperbolic space.
We address the question of whether a Riemannian manifold-with-boundary (M,g) in dimension two is uniquely determined from knowledge of the distances between points on its boundary. An affirmative answer is called boundary rigidity for…
We prove the scalar curvature rigidity for $L^\infty$ metrics on $\mathbb S^n\backslash\Sigma$, where $\mathbb S^n$ is the $n$-dimensional sphere with $n\geq 3$ and $\Sigma$ is a closed subset of $\mathbb S^n$ of codimension at least…
We take advantage of a rigidity result for the equation satisfied by an extremal function associated with a special case of the Caffarelli-Kohn-Nirenberg inequalities to get a symmetry result for a larger set of inequali-ties. The main…
We provide an introduction to logarithmic potential theory in the complex plane that particularly emphasizes its usefulness in the theory of polynomial and rational approximation. The reader is invited to explore the notions of Fekete…
Geodesic balls in a simply connected space forms $\mathbb{S}^n$, $\mathbb{R}^{n}$ or $\mathbb{H}^{n}$ are distinguished manifolds for comparison in bounded Riemannian geometry. In this paper we show that they have the maximum possible…
Let \mu be a computable ergodic shift-invariant measure over the Cantor space. Providing a constructive proof of Shannon-McMillan-Breiman theorem, V'yugin proved that if a sequence x is Martin-L\"of random w.r.t. \mu then the strong…
In this paper we derive topological and number theoretical consequences of the rigidity of elliptic genera, which are special modular forms associated to each compact almost complex manifold. In particular, on the geometry side, we prove…
The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are useful in the study of this question. In…