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We study the action of a real reductive group $G$ on a real submanifold $X$ of a Kahler manifold $Z$. We suppose that the action of a compact connected Lie group $U$ with Lie algebra $\mathfrak{u}$ extends holomorphically to an action of…

Consider the action of $GL(n,\mathbb{Q_p})$ on the $p$-adic unit sphere $\mathcal{S}_n$ arising from the linear action on $\mathbb{Q}_p^n\setminus\{0\}$. We show that for the action of a semigroup $\mathfrak{S}$ of $GL(n,\mathbb{Q}_p)$ on…

We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a result due to U. Hamenst\"{a}dt regarding finitely generated…

It is known that a finite group G can only act freely on affine n-space if K has positive characteristic p and G is a p-group. In that case the group action is "non-linear" and the ring of regular functions must be a trace-surjective…

For a semifield extension $T /S$, an action of a finite group $G$ on $T$ is Galois if $(1)$ the $G$-invariant subsemifield of $T$ is $S$ and $(2)$ subgroups of $G$ whose invariant semifields coincide are equal. We show that for a finite…

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1]…

In this paper we show that the transverse image of the momentum map of a Hamiltonian Lie group action admits a natural integral affine stratification with the property that over each stratum the momentum map is an equivariantly locally…

Let $({\sf G},\alpha, \omega,\mathfrak B)$ be a measurable twisted action of the locally compact group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a differential Banach $^*$-subalgebra of $\mathfrak B$, which is…

Let G be a locally compact group, let X be a universal proper G-space, and let Z be a G-equivariant compactification of X that is H-equivariantly contractible for each compact subgroup H of G. Let W be the resulting boundary. Assuming the…

We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate…

In this work we are concerned with the multiplicity of the eigenvalues of the Neumann Laplacian in regions of Rn which are invariant under the natural action of a compact subgroup G of O(n). We give a partial positive answer (in the Neumann…

We extend the Global Compactness result by M. Struwe (Math. Z, 1984) to any fractional Sobolev spaces $\dot{H}^s(\Omega)$ for $0<s<N/2$ and $\Omega \subset \mathbb{R}^N$ a bounded domain with smooth boundary. The proof is a simple direct…

We consider conformal actions of simple Lie groups on compact Lorentzian manifolds. Mainly motivated by the Lorentzian version of a conjecture of Lichnerowicz, we establish the alternative: Either the group acts isometrically for some…

We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for…

We consider an action of a countable amenable group on a compact metric space, focusing on the set of generic points with respect to a fixed F{\o}lner sequence. For a given characteristic class, we prove that the set of points that are…

Let $M$ be a factor with separable predual and $G$ a compact group of automorphisms of $M$ whose action is minimal, i.e. $M^{G^\prime}\cap M = C$, where $M^G$ denotes the $G$-fixed point subalgebra. Then every intemediate von Neumann…

A result by Ornstein and Weiss states that a free and measure-preserving action of an amenable group on a probability space yields a decomposition of the space in disjoint images, up to a small error, analogous to the one given by the…

We presented a Hilbert-Mumford criterion for polystablility associated with an action of a real reductive Lie group $G$ on a real submanifold $X$ of a Kahler manifold $Z$. Suppose the action of a compact Lie group with Lie algebra…

We establish a new connection between local and large-scale structure in compactly generated totally disconnected locally compact (t.d.l.c.) groups $G$, finding a sufficient condition for $G$ to have more than one end in terms of its…

Given a partial action of a topological group $G$ on a space $X$, we determine properties $\mathcal P$ which can be extended from $X$ to its globalization. We treat the cases when $\mathcal P$ is any of the following: Hausdorff, regular,…