Related papers: Coman conjecture for the bidisc

We provide a simple proof for the Fenchel duality between strong convexity and Lipschitz continuous gradient. To this end, we first establish equivalent conditions of convexity for a general function that may not be differentiable. By…

In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…

We prove a disc formula for the weighted Siciak-Zahariuta extremal function $V_{X,q}$ for an upper semicontinuous function $q$ on an open connected subset $X$ in $\C^n$. This function is also known as the weighted Green function with…

In this note we offer some log-concavity properties of certain functions related to Bessel functions of the first kind and modified Bessel functions of the first and second kind, by solving partially a recent conjecture on the…

For the $p$-harmonic function with strictly convex level sets, we find a test function which comes from the combination of the norm of gradient of the $p$-harmonic function and the smallest principal curvature of the level sets of…

We show an example of a sequence of elliptic operators in the unit ball with drifts that diverge as the inverse distance to the boundary, for which we do not get uniform upper estimates for the Green's function with the pole at the origin.…

We use the moment approach of Nolting (exact sum rules) (Z. Physik 255, 25 (1972)) for the attractive Hubbard model in the superconducting phase. Our diagonal and off - diagonal spectral functions are constructed and evaluated with the sum…

In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.

In connection to a conjecture of W. L\"u. Q. Li and C. Yang we prove a result on small function sharing by a power of a meromorphic function with few poles and its derivative. Our results improve a number of known results.

The Green's function, serving as a kernel function that delineates the interaction relationships of physical quantities within a field, holds significant research implications across various disciplines. It forms the foundational basis for…

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…

In this note we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Also a few Beurling type hitting estimates are obtained for the random walk on discretizations of…

This paper explores two generalizations of the classical Aubin-Lions Lemma. First we give a sufficient condition to commute weak limit and multiplication of two functions. We deduce from this criteria a compactness Theorem for degenerate…

We prove a recent conjecture of Hadjicostas concerning a double integral formula involving the zeta and the gamma functions.

In this paper, we prove a gap result for a locally conformally flat complete non-compact Riemannian manifold with bounded non-negative Ricci curvature and a scalar curvature average condition. We show that if it has positive Green function,…

We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence \{\lambda_k\}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we…

In this paper we obtain the explicit expression of the Green's function related to a general $n$ order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, a $n$ dimensional parameter…

For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the Gromov-Witten theories of the orbifold and the resolution. We prove the conjecture for the…

Lam, Lee, and Shimozono introduced the double Stanley symmetric functions in their study of the equivariant geometry of the affine Grassmannian. They proved that the associated double Edelman--Greene coefficients, the double Schur expansion…

We show that Connes' embedding conjecture (CEC) is equivalent to a real version of the same (RCEC). Moreover, we show that RCEC is equivalent to a real, purely algebraic statement concerning trace positive polynomials. This purely algebraic…