Related papers: Minimal Homeomorphisms on Low-Dimension Tori

Let G be a reductive group over an algebraically closed field of characteristic p, and let u in G be a unipotent element of order p. Suppose that p is a good prime for G. We show in this paper that there is a homomorphism phi:SL_2/k --> G…

We consider a finitely generated group acting minimally on a compact space by homeomorphsims, and assume that the Schreier graph of at least one orbit is quasi-isometric to a line. We show that the topological full group of such an action…

The minimal degree of a permutation group $G$ is the minimum number of points not fixed by non-identity elements of $G$. Lower bounds on the minimal degree have strong structural consequences on $G$. In 2014 Babai proved that the…

Consider a closed coisotropic submanifold $N$ of a symplectic manifold $(M,\omega)$ and a Hamiltonian diffeomorphism $\phi$ on $M$. The main result of this article states that $\phi$ has at least the cup-length of $N$ many leafwise fixed…

We study local biholomorphisms with finite orbits in some neighborhood of the origin since they are intimately related to holomorphic foliations with closed leaves. We describe the structure of the set of periodic points in dimension 2. As…

We consider classification problems for manifolds and discrete subgroups of Lie groups from a descriptive set-theoretic point of view. This work is largely foundational in conception and character, recording both a framework for general…

This paper is dedicated to the Orlicz-Petty bodies. We first propose the homogeneous Orlicz affine and geominimal surface areas, and establish their basic properties such as homogeneity, affine invariance and affine isoperimetric…

An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds. The present paper has two parts. The first part investigates topology of the isoparametric families, namely the…

We study the structure of tensor products of $\mathfrak{gl}(\infty) = \varinjlim \mathfrak{gl}(n)$-modules $\mathbf L(\mathbf \lambda) \otimes \mathbf F$ where $\mathbf L(\mathbf \lambda)$ is a simple integrable highest weight module and…

A set of locally finite perimeter $E \subset \mathbb{R}^{n}$ is called an anisotropic minimal surface in an open set $A$ if $\Phi(E;A) \le \Phi(F;A)$ for some surface energy $\Phi(E;A) = \int_{\partial^{*}E \cap A} \| \nu_{E}\| d…

Let $\G$ be a semisimple algebraic group defined over a number field $K$, $\te$ a maximal $K$-split torus of $\G$, $\mathcal{S}$ a finite set of valuations of $K$ containing the archimedean ones, $\OO$ the ring of $\mathcal{S}$-integers of…

We obtain constraints on the topology of families of smooth $4$-manifolds arising from a finite dimensional approximation of the families Seiberg-Witten monopole map. Amongst other results these constraints include a families generalisation…

The standard eigenfunctions $\phi_{\lambda} = e^{i < \lambda, x >}$ on flat tori $\R^n / L$ have $L^{\infty}$-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that $L^2$-normalized…

We focus on the presence of almost automorphy in strongly monotone skew-product semiflows on Banach spaces. Under the $C^1$-smoothness assumption, it is shown that any linearly stable minimal set must be almost automorphic. This extends the…

Let $M$ be a locally symmetric irreducible closed manifold of dimension $\ge 3$. A result of Borel [Bo] combined with Mostow rigidity imply that there exists a finite group $G = G(M)$ such that any finite subgroup of $\text{Homeo}^+(M)$ is…

In this paper, we extend the Goldman-Millson Theorem for $L_\infty$ algebras. We consider two $L_\infty$ algebras $L$ and $\tilde{L}$ endowed with descending, bounded above and complete filtrations compatible with the $L_\infty$ structures…

For a tropical manifold of dimension n we show that the tropical homology classes of degree (n-1, n-1) which arise as fundamental classes of tropical cycles are precisely those in the kernel of the eigenwave map. To prove this we establish…

We prove the LeBrun-Salamon Conjecture in low dimensions. More precisely, we show that a contact Fano manifold X of dimension 2n+1 that has reductive automorphism group of rank at least n-2 is necessarily homogeneous. This implies that any…

Let $\mathbb{U}$ be a Banach Lie group and $S\subseteq \mathbb{U}$ an ad-bounded subset thereof, in the sense that there is a uniform bound on the adjoint operators induced by elements of $S$ on the Lie algebra of $\mathbb{U}$. We prove…

Given a closed manifold $M$ and a closed regular submanifold $L$, consider the corresponding locally convex space $I=I(M,L)$ of conormal distributions, with its natural topology, and the strong dual $I'=I'(M,L)=I(M,L;\Omega)'$ of the space…