Related papers: Two local inequalities
We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic $3$-space and in de Sitter space. Several dualities of invariants are pointed out.
In this paper, we establish some integral ineuqalities for n- times differentiable quasi-convex functions.
This paper addresses the study and applications of polyhedral duality of locally convex topological vector (LCTV) spaces. We first revisit the classical Rockafellar's proper separation theorem for two convex sets one which is polyhedral and…
We present four counterexamples in surface homology. The first example shows that even if the loops inducing a homology basis intersect each other at most once, they still may separate the surface into two parts. The other three examples…
Zariski decompositions play an important role in the theory of algebraic surfaces. For making geometric use of the decomposition of a given divisor, one needs to pass to a multiple of the divisor in order to clear denominators. It is…
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
We provide a functional Rogers-Shephard type inequality for log-concave functions on $\mathbb R^n$ and any $1$-reducible $s$-cover of $[n]$. As a consequence, we derive a sharp local Liakopoulos-Meyer type inequality for $n$-dimensional…
We investigate the notion of the $p$-divisor for foliations on a smooth algebraic surface defined over a field of positive characteristic $p$ and we study some of their properties. We present a structure theorem for the $p$-divisor of…
In this paper some Hadamard_type inequalities for product of convex functions of 2-variables on the co-ordinates are given.
In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics.
Identities and inequalities for the cosine and sine functions are obtained.
In this note, we show that a part of [5, Remark 2.2] is not correct. Some conditions are given under which the same holds.
We investigate the average order of the divisor function at values of totally reducible binary cubic forms and discuss some applications.
We prove a new equidistribution estimate for the divisor function in arithmetic progression to moduli that have two small factors. We give two applications. First, we show an asymptotic formula for the divisor function over arithmetic…
We establish an inequality of different metrics for algebraic polynomials.
A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.
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.
In this short note, we extend the results of [Alexeev-Orlov, 2012] about Picard groups of Burniat surfaces with $K^2=6$ to the cases of $2\le K^2\le 5$. We also compute the semigroup of effective divisors on Burniat surfaces with $K^2=6$.…
In this paper, we formulate and prove Wendroff's inequalities on time scales. Next, we deduct some of Pachpatte's inequalities.
We present a generalization of the Bogomolov-Miyaoka-Yau inequality to Deligne-Mumford surfaces of general type.