Related papers: Bounds for the Euclidean minima of function fields

In recent years there has been great interest in variational analysis of a class of nonsmooth functions called the minimal time function. In this paper we continue this line of research by providing new results on generalized…

We give upper and lower bounds on the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian…

We extend the notion of $r$-minimality of a submanifold in arbitrary codimension to $u$-minimality for a multi-index $u\in\mathbb{N}^q$, where $q$ is the codimension. This approach is based on the analysis on the frame bundle of orthonormal…

We determine the minimal equivariant embedding dimension of orthgonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embedding dimension is achieved at isospectral model.

For a unit vector field on a closed immersed Euclidean hypersurface $M^{2n+1}$, $n\geq 1$, we exhibit a nontrivial lower bound for its energy which depends on the degree of the Gauss map of the immersion. When the hypersurface is the unit…

We described a minimal separating set for the algebra of $O(F_q)$-invariant polynomial functions of $m$-tuples of two-dimensional vectors over a finite field $F_q$.

We prove that the Gauss curvature and the curvature of the normal connection of any minimal surface in the four dimensional Euclidean space satisfy an inequality, which generates two classes of minimal surfaces: minimal surfaces of general…

We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine…

We establish general assumptions under which a constrained vari- ational problem involving the fractional gradient and a local nonlin- earity admits minimizers.

In this note, we show that the minmax and maxmin critical values of a function quadratic nondegenerate at infinity are equal when defined in homology or cohomology with coefficients in a field. However, by an example of F.Laudenbach, this…

We prove a function field analogue of Maynard's result about primes with restricted digits. That is, for certain ranges of parameters n and q, we prove an asymptotic formula for the number of irreducible polynomials of degree n over a…

We prove a scale-invariant boundary Harnack principle in inner uniform domains in the context of local regular Dirichlet spaces. For inner uniform Euclidean domains, our results apply to divergence form operators that are not necessarily…

We consider geometric variational problems for a functional defined on a curve in three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange…

Given a toric metrized R-divisor on a toric variety over a global field, we give a formula for the essential minimum of the associated height function. Under suitable positivity conditions, we also give formulae for all the successive…

We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…

In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributions. We give a constructive proof of the existence of minimal…

Stability version of the Prekopa-Leindler inequality for log-concave functions on the n-dimensional Euclidean space is established.

In this article, we give a proof for that the cardinality of a function basis of the invariants for a finite dimensional real vector space by a compact group is lower bounded by the intuitive difference of the dimensions of the vector space…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

We provide a development that unifies, simplifies and extends considerably a number of minimax results in the restricted parameter space literature. Various applications follow, such as that of estimating location or scale parameters under…