Related papers: Monotonicity results and bounds for the inverse hy…
Multilinear trace restriction inequalities are obtained for Hardy's inequality. More generally, detailed development is given for new multilinear forms for Young's convolution inequality, and a new proof for the multilinear…
We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev-Korobov-type smoothness and mixed Sobolev-analytic-type smoothness in the infinite-dimensional case where…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…
We consider an inverse boundary value problem for the hyperbolic partial differential equation $ (-i\partial_{t} + A_{0}(t,x))^2 u(t,x) - \sum_{j=1}^n (-i\partial_{x_j} + A_{j}(t,x))^2 u(t,x) + V(t,x)u(t,x) = 0 $ with time dependent vector…
We will provide bounds on both the Betti numbers and the torsion part of the homology of hyperbolic orbifolds. These bounds are linear in the volume and are a direct consequence of an efficient simplicial model of the thick part, which we…
We find a new monotone increasing quantity along smooth solutions to the inverse mean curvature flow in $\mathbb R^n$. As an application, we derive a sharp geometric inequality for mean convex, star-shaped hypersurfaces which relates the…
In this paper we investigate the monotonicity properties related to the ratio of gamma functions, from which some related asymptotics and inequalities are established. Some special cases also confirm the conjectures of C.-P. Chen…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Let $H_1$ and $H_2$ be selfadjoint operators or relations (multivalued operators) acting on a separable Hilbert space and assume that the inequality $H_1 \leq H_2$ holds. Then the validity of the inequalities $-H_1^{-1} \leq -H_2^{-1}$ and…
In the context of cubic splines, the authors have contributed to a recent paper dealing with the computation of nonlinear derivatives at the interior nodes so that monotonicity is enforced while keeping the order of approximation of the…
We review recent progress on two closely related sets of questions concerning convex co-compact hyperbolic manifolds, or convex domains in those manifolds, such as their convex core. The first set of questions is to what extent the…
Based on an assumption on the Hessian of the Green function, we derive some monotonicity formulas on nonparabolic manifolds. This assumption is satisfied on manifolds that meet certain conditions including bounds on the sectional curvature…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
We obtain bounds on hyperbolic volume for periodic links and Conway sums of alternating tangles. For links that are Conway sums we also bound the hyperbolic volume in terms of the coefficients of the Jones polynomial.
We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved…
In this paper, we first prove monotonicity of a generalized para bolic frequency on weighted closed Riemannian manifolds for some linear heat equation. Secondly, a certain generalized parabolic frequency functional is defined with respect…
This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control set of a hyperbolic linear control system in R^{d} this yields…
The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…