Related papers: Extending a rigidity result of Lytchak

Let $T$ be a compact, metrisable and strongly countable-dimensional topological space. Let $\mathcal{M}^T$ be the set of all metrics $d$ on $T$ compatible with its topology, and equip $\mathcal{M}^T$ with the topology of uniform…

Ratner's theorem implies topological rigidity of immersed totally geodesic subspaces of noncompact type in finite-volume locally symmetric spaces. In higher rank and infinite volume, however, counter-examples to this rigidity have remained…

In this paper we present alternative proofs for two known rigidity results concerning non-negatively curved compact biconservative hypersurfaces in space forms. Further, we prove some new rigidity results by replacing the hypothesis of…

This paper consists of three interconnected parts. Parts I,III study the relationship between the cohomology of a reductive group and that of a Levi subgroup. For example, we provide a necessary condition, arising from Kazhdan-Lusztig…

In this paper, we obtain a rigidity result of $2$-dimensional complete lagrangian self-shrinkers with constant squared norm $|\vec{H}|^{2}$ of the mean curvature vector in the Euclidean space $\mathbb{R}^{4}$. The same idea is also used to…

We prove necessary and sufficient conditions for a Calder\'on-Zygmund operator to be compact at the endpoint from $L^{1}(\mathbb R^{d})$ into $L^{1,\infty}(\mathbb R^{d})$.

Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{\"u}ller space. We notice that…

We extend to infinite dimensional Hilbert spaces a celebrated result, due to B. Polyak, about the convexity of the joint image of quadratic functions. We give sufficient conditions which assure that the joint image is also closed. However,…

We present a condition for automatic O$(a)$ improvement in twisted mass lattice QCD, using symmetries of the Symanzik effective theory. If the continuum part of the Symanzik effective theory is invariant under a particular transformation,…

We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The r\^ole of the metric is taken over by the time separation function, in terms of which all basic notions are…

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in…

In this paper we show how a natural coupling of the Dirac equation with the generalized Jang equation, leads to a proof of the rigidity statement in the positive mass theorem with charge, without the maximal slicing condition, provided a…

We present a coordinate-free version of Fefferman's solution of Whitney's extension problem in the space $C^{m-1,1}(\mathbb{R}^n)$. While the original argument relies on an elaborate induction on collections of partial derivatives, our…

We study affine maps between CAT(0) spaces with geometric actions, and show that they essentially split as products of dilations and linear maps (on the Euclidean factor). This extends known results from the Riemannian case. Furthermore, we…

We extend the polydisk theorem of [21], originally established for classical Cartan-Hartogs domains, to Hartogs domains over arbitrary (possibly reducible and exceptional) bounded symmetric domains. We further establish a dual counterpart…

We look at $d$-point extensions of a rotation of angle $\alpha$ with $r$ marked points, generalizing the examples of Veech 1969 and Sataev 1975, together with the square-tiled interval exchange transformations of \cite{fh2}. We study the…

The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike…

We study scattering rigidity in Lorentzian geometry: recovery of a Lorentzian metric from the scattering relation $\mathcal{S}^\sharp$ known on a lateral boundary. We show that, under a non-conjugacy assumption, every defining function…

Let $C$ be a subset of $\mathbb{R}^n$ (not necessarily convex), $f:C\to\mathbb{R}$ be a function, and $G:C\to\mathbb{R}^n$ be a uniformly continuous function, with modulus of continuity $\omega$. We provide a necessary and sufficient…

We consider various notions of completeness in symplectic topology and ask two related questions. Does a complete open symplectic manifold remain complete after excising a subset? Can two sets be made arbitrarily far apart by adjusting the…