Related papers: Estimates for the Bergman Kernel and the Multidime…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…

We produce a criterion for open sets in projective $n$-space over a separably closed field to have \'etale cohomological dimension bounded by $2n-3$. We use the criterion to exhibit a scheme for which \'etale cohomological dimension is…

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…

We investigate the gauging of the Wess-Zumino term of a sigma model with boundary. We derive a set of obstructions to gauging and we interpret them as the conditions for the Wess-Zumino term to extend to a closed form in a suitable…

The purpose of this paper is to establish a subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As applications, we obtain a product formula of the restricted canonical volumes for algebraic fiber spaces and a sufficient…

Given a knot in 3-space, one can associate a sequence of Laurrent polynomials, whose $n$th term is the $n$th colored Jones polynomial. The Generalized Volume Conjecture states that the value of the $n$-th colored Jones polynomial at $\exp(2…

The well--known Freiman--Ruzsa Theorem provides a structural description of a set $A$ of integers with $|2A|\le c|A|$ as a subset of a $d$--dimensional arithmetic progression $P$ with $|P|\le c'|A|$, where $d$ and $c'$ depend only on $c$.…

Affine su(3) and su(4) fusion multiplicities are characterised as discretised volumes of certain convex polytopes. The volumes are measured explicitly, resulting in multiple sum formulas. These are the first polytope-volume formulas for…

Here we prove some special cases of the following conjecture: that the sum of the Betti numbers of a 1-connected elliptic space is greater than the total rank of its homotopy groups. Our main tool is Sullivan's minimal model.

We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…

In this note we shall prove that the complete K\"{a}hler-Einstein volume form on a bounded strongly pseudoconvex domain with $C^{\infty}$-boundary is the normalized limit of a sequence of Bergman kernels.

Let $A_\zeta=\Omega-\overline{\rho(\zeta)\cdot\Omega}$ be a family of generalized annuli over a domain $U$. We show that the logarithm $\log K_{\zeta}(z)$ of the Bergman kernel $K_{\zeta}(z)$ of $A_\zeta$ is plurisubharmonic provided…

In convex geometry, the Blaschke surface area measure on the boundary of a convex domain can be interpreted in terms of the complexity of approximating polyhedra. In response to a question raised by D. Barrett, this approach is formulated…

We provide a natural generalization of a geometric conjecture of F\'{a}ry and R\'{e}dei regarding the volume of the convex hull of $K \subset {\mathbb R}^n$, and its negative image $-K$. We show that it implies Godbersen's conjecture…

Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…

We obtain a quantitative estimate of Bergman distance when $\Omega \subset \mathbb{C}^n$ is a bounded domain with log-hyperconvexity index $\alpha_l(\Omega)>\frac{n-1+\sqrt{(n-1)(n+3)}}{2}$, as well as the $A^2(\log A)^q$-integrability of…

Combining the tools of geometric analysis with properties of Jordan angles and angle space distributions, we derive a spherical and a Euclidean Bernstein theorem for minimal submanifolds of arbitrary dimension and codimension, under the…

We compute explicitly the Bergman kernels of all two dimensional monomial polyhedra, a class of domains including the Hartogs triangle and some of its generalizations. The kernel is computed from the representation of such domains as…

Two sharp comparison results are derived for three-dimensional complete noncompact manifolds with scalar curvature bounded from below. The first one concerns the Green's function. When the scalar curvature is nonnegative, it states that the…