Related papers: On the paper "A study on concave optimization via …
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
In this article, we first describe codimension two regular foliations with numerically trivial canonical class on complex projective manifolds whose canonical class is not numerically effective. Building on a recent algebraicity criterion…
We present a probabilistic interpretation of several functional isoperimetric inequalities within the class of $p$-concave functions, building on random models for such functions introduced by P. Pivovarov and J. Rebollo-Bueno. First, we…
In this paper, we show that the minimal model theory does not hold in characteristic two. More precisely, we construct counter-examples to the relative abundance conjecture.
We provide a new and significantly shorter optimality proof of recent quantified Tauberian theorems, both in the setting of vector-valued functions and of $C_0$-semigroups, and in fact our results are also more general than those currently…
In Theorem 1.2 of the paper math.GT/0002110 the author claimed to have proved that all transversal knots whose topological knot type is that of an iterated torus knot (we call them cable knots) are transversally simple. That theorem is…
It is shown that the arguments in the reply of Z.-D. Zhang (arXiv:0812.0194) to the comment arXiv:0811.1802 defending his conjectures in arXiv:0705.1045 are invalid. His conjectures have been thoroughly disproved.
We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent results about Lusin approximation of convex functions and…
We discuss the cone and contraction theorem in a suitable complex analytic setting. More precisely, we establish the cone and contraction theorem of normal pairs for projective morphisms between complex analytic spaces. This result is a…
This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.
We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].
The property 4 in Proposition 2.3 from the paper "Some remarks on Davie's uniqueness theorem" is replaced with a weaker assertion which is sufficient for the proof of the main results. Technical details and improvements are given.
This paper has been withdrawn by the authors, due to an error in the proof of Lemma 3.1.
With this note we bring again into attention a vector dual problem neglected by the contributions who have recently announced the successful healing of the trouble encountered by the classical duals to the classical linear vector…
A recent theorem of Diverio--Trapani and Wu--Yau asserts that a compact K\"ahler manifold with a K\"ahler metric of quasi-negative holomorphic sectional curvature is projective and canonically polarized. This confirms a long-standing…
Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and…
Theorem 2 of A. Kercheval, "Denjoy minimal sets are far from affine", Ergodic Theory and Dynamical Systems 22 (2002), 1803-1812 is corrected by adding a C^2 bound to the hypotheses.
We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and…
Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…
This paper has been withdrawn, as all conjectures (and one claim) have been proven incorrect. Some of what remains may eventually reappear in a different context.