相关论文: The Variable Radius Form of the Extended Exterior …

We study the multiplicity problem for prime closed orbits of dynamically convex Reeb flows on the boundary of a star-shaped domain in $\mathbb{R}^{2n}$. The first of our two main results asserts that such a flow has at least $n$ prime…

We prove a new rigidity result for an open manifold M with nonnegative sectional curvature whose soul S is odd-dimensional. Specifically, there exists a geodesic in S and a parallel vertical plane field along it with constant vertical…

We derive slow-roll conditions for a scalar field which is non-minimally coupled with gravity in a consistent manner and express spectral indices of scalar/tensor perturbations in terms of the slow-roll parameters. The conformal invariance…

We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.

In this article we proved an interesting property of the class of continuous convex functions. This leads to the form of pre-Hermite-Hadamard inequality which in turn admits a generalization of the famous Hermite-Hadamard inequality. Some…

This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…

In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…

We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher…

We define an interesting sub-category of the category of simplicial sets, $\Sr$, whose objects are called regular. Both it and the subcategory ${\cal S}_{f-{\rm reg}}$ of finite regular simplicial sets have good stability properties under…

Similarly to the classic notion in $E^d$, a subset of a positive diameter below $\frac{\pi}{2}$ of a hemisphere of the sphere $S^d$ is called complete, provided adding any extra point increases its diameter. Complete sets are convex bodies…

While intersections of convex sets are convex, their unions have rather complicated behavior. Some natural contexts where they appear include duality arguments involving boundaries of convex sets and valuations, which have an Euler…

Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb{R}^{d})$ called a potential we define its rotation set $R(F)$ as the set of integrals of $F$ with respect to all $T$-invariant…

We prove explicit lower bounds for the smallest singular value and upper bounds for the condition number of rectangular, multivariate Vandermonde matrices with scattered nodes on the complex unit circle. Analogously to the Shannon-Nyquist…

In this work we consider the Landau-de Gennes model for liquid crystals with an external electromagnetic field to model the occurrence of the saturn ring effect under the assumption of rotational equivariance. After a rescaling of the…

Variational convexity, together with ist strong counterpart, of extended-real-valued functions has been recently introduced by Rockafellar. In this paper we present second-order characterizations of these properties, i.e., conditions using…

We explore the phenomenon of cavitation in higher-dimensional elasticity, defining it as the mapping of a punctured ball onto a non-degenerate ring domain. Crucially, for the class of locally quasiconformal mappings (or more general…

Let an $R$-body be the complement of the union of open balls of radius $R$ in $\mathbb{E}^d$. The $R$-hulloid of a closed not empty set $A$, the minimal $R$-body containing $A$, is investigated; if $A$ is the set of the vertices of a…

In this article, we investigate the range characterization for the spherical mean transform (SMT) of functions supported in the unit ball. In earlier works, in the case of odd dimensions, a set of differential conditions was obtained,…

We generalize the time-honored Weinberg's compositeness relations by including the range corrections through considering a general form factor. In Weinberg's derivation, he considered the effective range expansion up to $\mathcal{O}(p^2)$…

We present dynamic equations for two dimensional closed surfaces and analytically solve it for some simplified cases. We derive final equations for surface normal motions by two different ways. The solution of the equations of motions in…