Zahl, Joshua
Published in
Geometric and Functional Analysis

In 1901, Severi proved that if Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{Z}}$$\end{document} is an irreducible hypersurface in P4(C)\documentclass[12pt]{minima...

Colombo, Maria Spolaor, Luca Velichkov, Bozhidar
Published in
Geometric and Functional Analysis

We study the regularity of the regular and of the singular set of the obstacle problem in any dimension. Our approach is related to the epiperimetric inequality of Weiss (Invent Math 138:23–50, Wei99a), which works at regular points and provides an alternative to the methods previously introduced by Caffarelli (Acta Math 139:155–184, Caf77). In his...

Mrowka, Tomasz S. Wehrheim, Katrin
Published in
Geometric and Functional Analysis

We examine the L2-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl lemma of harmonic analysis, and deduce local pathwise connectedness of the gauge orbits. Based on a quantitative version of the connectivity, we generalize compactness results for anti-self-dual instantons with L...

Gaspar, Pedro Guaraco, Marco A. M.
Published in
Geometric and Functional Analysis

We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich–Marques–Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie–Marques–Neves and Marques–Neves–Song, respectively. We also prove the density of sepa...

Rudelson, Mark Tikhomirov, Konstantin
Published in
Geometric and Functional Analysis

The circular law asserts that the empirical distribution of eigenvalues of appropriately normalized n×n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n \times n}$$\en...

Li, Qiongling
Published in
Geometric and Functional Analysis

Let (S,g0) be a hyperbolic surface, ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho}$$\end{document} be a Hitchin representation for PSL(n,R)\documentclass[12pt]...

Gekhtman, Ilya Levit, Arie
Published in
Geometric and Functional Analysis

Let X be a proper geodesic Gromov hyperbolic metric space and let G be a cocompact group of isometries of X admitting a uniform lattice. Let d be the Hausdorff dimension of the Gromov boundary ∂X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs...

Jaikin-Zapirain, Andrei
Published in
Geometric and Functional Analysis

Let F be a free finitely generated group and A∈Matn×m(C[F])\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {\rm Mat}_{n \times m}(\mathbb{C}[F])}$$\end{document}...

Fu, Joseph H.G. Wannerer, Thomas
Published in
Geometric and Functional Analysis

A famous theorem of Weyl states that if M is a compact submanifold of euclidean space, then the volumes of small tubes about M are given by a polynomial in the radius r, with coefficients that are expressible as integrals of certain scalar invariants of the curvature tensor of M with respect to the induced metric. It is natural to interpret this ph...

Haim-Kislev, Pazit
Published in
Geometric and Functional Analysis

In this paper we introduce a combinatorial formula for the Ekeland–Hofer–Zehnder capacity of a convex polytope in R2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\m...