Related papers: Loxodromic unit vector field on punctured spheres

We prove that a functional with Lipschitzian derivative, when restricted to suitable spheres centered at a noncritical point, has a unique maximum.

For $L$-functions attached to automorphic representations of unitary groups $U_{n+1}\times U_n$, we establish a subconvex bound valid in certain horizontal aspects, where the set of ramified places is allowed to vary.

In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an $n$-dimensional Euclidean space and obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine…

A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. The valuations are classified in terms of their behaviour with…

We prove that the half-integer valued local index of an isolated umbilic point on a $C^{3+\alpha}$-smooth convex surface in Euclidean 3-space is less than two. The approach is to study the co-kernel of an associated Riemann-Hilbert boundary…

This paper investigates properties of complex-valued eigenvalue trajectories for the interior transmission problem parametrized by the index of refraction for homogeneous media. Our theoretical analysis for the unit disk shows that the only…

We consider one dimensional holomorphic foliations with isolated singularities that leave invariant a local complete intersection. We establish explicit formulas for the total GSV index of such foliations and obtain bounds for this index.…

A general scheme of construction and analysis of physical fields on the various homogeneous spaces of the Poincar\'{e} group is presented. Different parametrizations of the field functions and harmonic analysis on the homogeneous spaces are…

We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we complete the classification of infinitesimal symmetries of…

This paper presents a new reformulated theorem for fields embedded on a sphere or a disk. We focus in particular on the associated sphere of a disk when closing its only one boundary. We call this the disk-sphere duality theorem for the…

We consider ruled and quadric surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form $III$, i.e., their position vector $\boldsymbol{x}$ satisfies the relation $\Delta…

Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a monoidal category of BPS line defects. Any Coulomb vacuum of such a theory can be conjecturally associated to an ``algebra of BPS…

Let $P$ be a simplicial smooth Fano polytope. We provide a concrete unimodular triangulation of $P$. We prove that the delta-vector of a simplicial smooth Fano polytope is unimodal and we give upper and lower bound for the volume of…

We prove bounds for the volume of neighborhoods of algebraic sets, in the euclidean space or the sphere, in terms of the degree of the defining polynomials, the number of variables and the dimension of the algebraic set, without any…

We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.

In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansion. This estimate is an analog of a result previously obtained by…

We show that the conjectural cusped complex hyperbolic 2-orbifolds of minimal volume are the two smallest arithmetic complex hyperbolic 2-orbifolds. We then show that every arithmetic cusped complex hyperbolic 2-manifold of minimal volume…

We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume the domain has a boundary with positive reach. We propose a data splitting approach to correct…

This paper investigates the geometry of smooth canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the…

Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le-Murakami-Ohtsuki invariant of homology three-spheres to a functor from the…