Related papers: A Result on Relative Conormal Spaces

This thesis is concerned with equidistant foliations of Euclidean space, i.e. partitions into complete, connected, properly embedded smooth submanifolds. The space of leaves is an Alexandrov space of nonnegative curvature and the canonical…

In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…

Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated . The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms…

Consider a multimodal interval map $f$ of $C^3$ with non-flat critical points. We establish several characterizations of the map $f$ is quasi-symmetrically conjugated to a piecewise affine map in the case $f$ is topologically exact and all…

We formulate a conjectural Lefschetz formula for locally symmetric spaces of finite volume. The formula can be verified in the compact case and for Riemann surfaces.

In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…

We study commutative associative polynomial operations $\mathbb{A}^n\times\mathbb{A}^n\to\mathbb{A}^n$ with unit on the affine space $\mathbb{A}^n$ over an algebraically closed field of characteristic zero. A classification of such…

We consider the distance to the nearest integer of f(p), where f is a quadratic polynomial with irrational leading coefficient. This distance is very small as a function of p, for infinitely many primes p. We give a 14% improvement in the…

The paper gives a historical survey of the causal position space renormalization with a special attention to the role of Raymond Stora in the development of this subject. Renormalization is reduced to subtracting the pole term in…

In this article, we give a simple explicit construction of an affine slice for the coadjoint action of a certain class of biparabolic (also called seaweed) subalgebras of a semisimple Lie algebra over an algebraically closed field of…

We present various results on the equivalence and mapping properties under affine transformations of fractional-order Sobolev norms and semi-norms of orders between zero and one. Main results are mutual estimates of the three semi-norms of…

The authors gave an affine isoperimetric inequality \cite{LYZ2010} that gives a lower bound for the volume of a polar body and the equality holds if and only if the body is a simplex. In this paper, we give a functional isoperimetric…

In this paper, we introduce and study the locally strongly convex equiaffine isoparametric hypersurfaces and equiaffine isoparametric functions on the affine space $A^{n+1}$. Motivated by the case on the Euclidean space $E^{n+1}$, we first…

In this note, we establish a duality result under the residue paring between certain two-dimensional adelic spaces, which are associated to a closed point on an arithmetic surface.

We prove local inequalities for analytic functions defined on a convex body in $\Re^{n}$ which generalize well-known classical inequalities for polynomials.

For every affine variety over a global function field, we show that the set of its points with coordinates in an arbitrary rank-one multiplicative subgroup of this function field is topologically dense in the set of its points with…

Let $\cal{P}$ be an affine invariant property of functions $\mathbb{F}_p^n \to [R]$ for fixed $p$ and $R$. We show that if $\cal{P}$ is locally testable with a constant number of queries, then one can estimate the distance of a function $f$…

Let $V$ be a vector space over a finite field $k$. We give a condition on a subset $A \subset V$ that allows for a local criterion for checking when a function $f:A \to k$ is a restriction of a polynomial function of degree $<m$ on $V$. In…

We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…

It is shown that a band limited function on a non-compact symmetric space can be reconstructed in a stable way from some countable sets of values of its convolution with certain distributions of compact support. A reconstruction method in…