Related papers: Sharp decouplings for three dimensional manifolds …

We extend the decoupling results of the first two authors to the case of real analytic surfaces of revolution in $\mathbb{R}^3$. New examples of interest include the torus and the perturbed cone.

This is a survey on the classification of smooth surfaces in P^4 and smooth 3-folds in P^5. We recall the corresponding results arising from adjunction theory and explain how to construct examples via syzygies. We discuss some examples in…

This is an example on the cohomology of threefolds.

We prove the sharp mixed norm $(l^2, L^{q}_{t}L^{r}_{x})$ decoupling estimate for the paraboloid in $d + 1$ dimensions.

We classify compact simply-connected 5-dimensional manifolds which admit a metric of nonnegative curvature with a connected non-abelian group acting by isometries. We show that they are diffeomorphic to either S^5, S^3 x S^2, the nontrivial…

We study structures of embedded projective manifolds swept out by cubic varieties. We show if an embedded projective manifold is swept out by high-dimensional smooth cubic hypersurfaces, then it admits an extremal contraction which is a…

In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.

We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting.

We study the space of deformations of a smooth foliation of the 5-sphere by complex manifolds

We prove boundedness of rationally-connected threefolds in $\mathbb P^6$ under some extra-assumptions.

It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the three-dimensional complex space. We show in fact that a one-dimensional submanifold of a closed orientable 3-manifold can be realised…

We prove an $l^p$ decoupling inequality for hypersurfaces with nonzero Gaussian curvature and use it to derive a corresponding $l^p$ decoupling for curves not contained in a hyperplane. This extends our earlier work from [2]

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…

We prove an effective version of a theorem relating curve complex distance to electric distance in hyperbolic 3-manifolds, up to errors that are polynomial in the complexity of the underlying surface. We use this to give an effective proof…

We prove a sharp lower bound on the curvatures of non-flat ASD connections over the cylinder.

By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3-manifolds are realized as transverse intersections of complex surfaces in complex 3-space with strictly…

We prove two types of results. First we develop the decoupling theory for hypersurfaces with nonzero Gaussian curvature, which extends our earlier work from \cite{BD3}. As a consequence of this we obtain sharp (up to $\epsilon$ losses)…

We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.

We define a new combinatorial class of triangulations of closed 3-manifolds, satisfying a weak version of 0-efficiency combined with a weak version of minimality, and study them using twisted squares. As an application, we obtain strong…

We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds…