Related papers: Bogomolov unstability on arithmetic surfaces

We present a relative form of the Toponogov comparison theorem.

In this paper, we present a variant of the Balog-Szemer\'edi-Gowers theorem for the Vinogradov system. We then use our result to deduce a higher degree analogue of the sum-product phenomenon.

An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.

We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.

In this paper, we establish the Zariski decompositions of arithmetic R-divisors of continuous type on arithmetic surfaces and investigate several properties. We also develop the general theory of arithmetic R-divisors on arithmetic…

In this note, we would like to propose a suitable extension of the arithmetic Chow group of codimension one, in which the Hodge index theorem holds. We also prove an arithmetic analogue of Bogomolov's instability theorem for rank 2 vector…

An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension…

We establish an inequality of different metrics for algebraic polynomials.

We prove a stability version of the Pr\'ekopa-Leindler inequality.

We give an elementary obstruction to reducibility for knotted surfaces in the four-sphere. As a new application, we construct stably irreducible non-orientable surfaces.

In this paper we prove Ulyanov-type inequalities between mixed moduli of smoothness of positive orders in different metrics.

We prove a sharp logarithmic Sobolev inequality which holds for submanifolds in Euclidean space of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature.

We shall give a refinement of the arithmetic-geometric mean inequality.

For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of…

We derive analogues of the classical Rayleigh, Fjortoft and Arnold stability and instability theorems in the context of the 2D $\alpha$-Euler equations.

We prove Gagliardo-Nirenberg inequalities on some classes of manifolds, Lie groups and graphs.

An adaptive analogue of the Yu. E. Nesterov method for variational inequalities with a strongly monotone operator is proposed. Some estimates are obtained for the parameters determining the quality of the solution of the variational…

Application of the "hairy ball theorem" to the analysis of the surface instabilities inherent for liquid/vapor interfaces is reported. When a continuous tangential velocity field exists on the surface of the liquid sample which is…

In this paper, we prove the Bogomolov-Gieseker type inequality conjecture for threefolds with nef tangent bundles. As a corollary, there exist Bridgeland stability conditions on these threefolds.

A version of Markov's estimate for the derivative of a polynomial is proved with the interval [-1,1] replaced by an arbitrary continuum in the complex plane.