We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak’s -Minkowski problem on which were obtained by other methods.
An infinite graph is said to be highly connected if the induced subgraph on the complement of any set of vertices of smaller size is connected. We continue the study of weaker versions of Ramsey’s theorem on uncountable cardinals asserting that if we c…
We study systems of two-tangle equations which play an important role in the analysis of enzyme actions on DNA strands.We show that every system of framed tangle equations has at most one-framed rational solution. Furthermore, we show that the Jones un…
In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with sum of lines as boundary divisors, and prove that for , these K-moduli of…
To every finite metric space X, including all connected unweighted graphs with the minimum edge-distance metric, we attach an invariant that we call its blowup-polynomial . This is obtained from the blowup – which contains copies of each point x – by…
Let be a finitely generated subgroup. Denote by its division group. A recent conjecture due to Rémond, related to the Zilber–Pink conjecture, predicts that the absolute logarithmic Weil height of an element of is bounded from below by a positive con…
Let be a complex simple Lie algebra and the nilradical of a parabolic subalgebra of . We consider some properties of the coadjoint representation of and related algebras of invariants. This includes (i) the problem of existence of generic stabilizer…
We use the dual functional realization of loop algebras to study the prime irreducible objects in the Hernandez–Leclerc (HL) category for the quantum affine algebra associated with . When the HL category is realized as a monoidal categorification of a …
For every , Bourgain’s constant is the largest number such that the (upper) Hausdorff dimension of harmonic measure is at most for every domain in on which harmonic measure is defined. Jones and Wolff (1988, Acta Mathematica 161, 131–144) proved tha…
This paper introduces type P web supercategories. They are defined as diagrammatic monoidal -linear supercategories via generators and relations. We study the structure of these categories and provide diagrammatic bases for their morphism spaces. We al…