Related papers: Mean action and the Calabi invariant

A theorem of Moser guarantees that every diffeomorphism of a closed manifold can be isotoped to a volume preserving one. We show that this statement cannot be extended into contact category: some connected components of contactomorphism…

This short note shows a limiting behavior of integrals of some centered antipersistent stationary infinitely divisible moving averages as the compact integration domain in $d\ge 1$ dimensions extends to the whole positive quadrant…

Let $M$ be a connected orientable compact surface, $f:M\to\mathbb{R}$ be a Morse function, and $\mathcal{D}_{\mathrm{id}}(M)$ be the group of difeomorphisms of $M$ isotopic to the identity. Denote by $\mathcal{S}'(f)=\{f\circ h = f\mid…

We show recurrent phenomena for orbits of groups of local complex analytic diffeomorphisms that have a certain subgroup or image by a morphism of groups that is non-virtually solvable. In particular we prove that a non-virtually solvable…

Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and centered at the origin, and from each circle contained in U…

The (local) invariant symplectic action functional $\A$ is associated to a Hamiltonian action of a compact connected Lie group $\G$ on a symplectic manifold $(M,\omega)$, endowed with a $\G$-invariant Riemannian metric $<\cdot,\cdot>_M$. It…

The behavior near the boundary in the Deligne-Mumford compactification of many functions on the moduli space of pointed Riemann surfaces can be conveniently expressed using the notion of "point-like limit" that we adopt from the string…

We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by $C^1$ diffeomorphisms of the closed interval with no global fixed…

Let $G\curvearrowright M$ be an isometric action of a Lie Group on a complete orientable Riemannian manifold. We disintegrate absolutely continuous measures with respect to the volume measure of $M$ along the principal orbits of…

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it…

In this paper, we study the regularized mean curvature flow starting from invariant hypersurfaces in a Hilbert space equipped with an isometric almost free Hilbert Lie group action whose orbits are minimal regularizable submanifolds, where…

Let $G$ be a Lie group and let $M$ be a proper smooth $G$-manifold. If $M$ is connected and $\dim(M)\geq 2$, the group of diffeomorphisms of $M$, that are isotopic to the identity through a compactly supported isotopy, acts $n$-transitively…

Given any smooth circle diffeomorphism with irrational rotation number, we show that its invariant probability measure is the only invariant distribution (up to multiplication by a real constant). As a consequence of this, we show that the…

We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at…

Let $M$ be the circle or a compact interval, and let $\alpha=k+\tau\ge1$ be a real number such that $k=\lfloor \alpha\rfloor$. We write $\mathrm{Diff}_+^{\alpha}(M)$ for the group of $C^k$ diffeomorphisms of $M$ whose $k^{th}$ derivatives…

Let $\|\cdot\|_{\mathbf A}$ be a norm on $\mathbb C^m$ given by the formula $\|(z_1,\ldots,z_m)\|_{\mathbf A}=\|z_1A_1+\cdots+z_mA_m\|_{\rm op}$ for some choice of an $m$-tuple of $n\times n$ linearly independent matrices $\mathbf A=(A_1,…

We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a…

We establish rigidity results for holomorphic mappings and plurisubharmonic functions in complex geometry. First, under mild conditions, we show that the gradient of a $\operatorname{U}(1)$-invariant strictly plurisubharmonic function in…

We consider finitely generated groups of real-analytic circle diffeomorphisms. We show that if such a group admits an exceptional minimal set (i.e., a minimal invariant Cantor set), then its Lebesgue measure is zero; moreover, there are…

We consider the boundary dynamics of iterated function systems of holomorphic self-maps of the unit disc. Our main result provides a sufficient condition which guarantees that the dynamical behaviour of a left iterated function system in…