Related papers: Obstruction Flat Rigidity of the CR 3-Sphere

Given $k\in \mathbb{R},$ $v,$ $D>0,$ and $n\in \mathbb{N},$ let $\left\{ M_{\alpha }\right\} _{\alpha =1}^{\infty }$ be a Gromov-Hausdorff convergent sequence of Riemannian $n$--manifolds with sectional curvature $\geq k,$ volume $>v,$ and…

We investigate the local deformation space of 3-dimensional cone-manifold structures of constant curvature $\kappa \in \{-1,0,1\}$ and cone-angles $\leq \pi$. Under this assumption on the cone-angles the singular locus will be a trivalent…

We prove that the image of an isometric embedding into ${\mathbb R}^3$ of a two dimensionnal complete Riemannian manifold $(\Sigma, g)$ without boundary is a convex surface provided both the embedding and the metric $g$ enjoy a…

A complex filling of a CR manifold is said to be equivariant with respect to a CR action if the action extends to a smooth action by biholomorphisms on the whole filling. Under a noncompactness condition for the action, we describe all…

The boundary rigidity problem is a classical question from Riemannian geometry: if $(M, g)$ is a Riemannian manifold with smooth boundary, is the geometry of $M$ determined up to isometry by the metric $d_g$ induced on the boundary…

The Q-curvature has been playing a central role in conformal geometry since its discovery by T. Branson. It has natural analogy in CR geometry, however, the CR Q-curvature vanishes on the boundary of a strictly pseudoconvex domain in…

The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a…

Let $M$ be a compact abstract $CR$ manifold of arbitrary $CR$ codimension. Under certain conditions on the Levi form we prove the infinite dimensionality of some global cohomology groups of $M$.

We extend the notions of CR GJMS operators and Q-curvature to the case of partially integrable CR structures. The total integral of the CR Q-curvature turns out to be a global invariant of compact nondegenerate partially integrable CR…

Following Ghomi and Tabachnikov we study topological obstructions to totally skew embeddings of a smooth manifold M in Euclidean spaces. This problem is naturally related to the question of estimating the geometric dimension of the stable…

We prove several theorems concerning the connection between the local CR embeddability of 3-dimensional CR manifolds, and the existence of algebraically special Maxwell and gravitational fields. We reduce the Einstein equations for…

The entanglement entropy of an arbitrary spacetime region $A$ in a three-dimensional conformal field theory (CFT) contains a constant universal coefficient, $F(A)$. For general theories, the value of $F(A)$ is minimized when $A$ is a round…

A conjecture due to Gompf asserts that no nontrivial Brieskorn homology sphere admits a pseudoconvex embedding in ${\mathbb C}^2$, with either orientation. A related question asks whether every compact contractible 4-manifold admits the…

The study of stable minimal surfaces in Riemannian $3$-manifolds $(M, g)$ with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when $(M, g)$ is asymptotically flat and has horizon…

We give an example of a compact Levi-flat CR 3-manifold with a positive-along-leaves CR line bundle which is not ample with respect to transversely infinitely differentiable CR sections. This example shows that we cannot improve the…

Graphs triangulating the $2$-sphere are generically rigid in $3$-space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a \emph{finite} subset $A$ in $3$-space so that the vertices of each graph $G$ as above can be mapped into $A$ to…

Let M be a closed embedded minimal hypersurface in a Euclidean sphere of dimension n+1, we prove that it is strongly rigid. As applications we confirm the conjecture proposed by Choi and Schoen in [3] and the Chern conjecture for n less…

Very few examples of obstructed equsingular families of curves on surfaces other than the projective plane are known. Combining results from Westenberger and Hirano with an idea from math.AG/9802009 we give in the present paper series of…

We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…

We exhibit a distinctly low-dimensional dynamical obstruction to the existence of Liouville cobordisms: for any contact 3-manifold admitting an exact symplectic cobordism to the tight 3-sphere, every nondegenerate contact form admits an…