Related papers: The canonical foliation on null hypersurfaces in l…

Let M be a complete simply connected Riemannian manifold, with sectional curvature K bounded above by -1. Under some assumptions on the geometry of the boundary of M, which are satisfied for instance if M is a symmetric space, or has…

We prove a splitting theorem for Riemannian n-manifolds with scalar curvature bounded below by a negative constant and containing certain area-minimising hypersurfaces (Theorem 3). Thus we generalise [25,Theorem 3] by Nunes. This splitting…

We establish a localized Bochner-type rigidity theorem for harmonic maps between Riemannian manifolds. Let $f : (M,g) \to (\overline{M},\overline{g})$ be a harmonic map from a compact manifold. Instead of assuming a global nonpositivity…

We consider the sub-Riemannian metric $g_{h}$ on $\mathbb{S}^3$ provided by the restriction of the Riemannian metric of curvature 1 to the plane distribution orthogonal to the Hopf vector field. We compute the geodesics associated to the…

We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC…

We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first…

As is well-known, there exist nonconstant holomorphic maps from the plane into the Riemann sphere $\PP^1$ minus two points, the simplest example of which is an explicit realization of the uniformization map given by applying the exponential…

We prove that a surface of prescribed mean curvature ($H$-surface) with free boundary on a two-dimensional $C^2$-manifold belongs to $C^{1,\frac{1}{2}}$ up to that the boundary, provided it is a-priori continuous. We allow the $H$-surface…

In this paper, we investigate the mean curvature flows starting from all non-minimal leaves of the isoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean…

We prove the existence of resolution of singularities for arbitrary (not necessarily reduced or irreducible) excellent two-dimensional schemes, via permissible blow-ups. The resolution is canonical, and functorial with respect to…

This paper extends the results of [GLS24], where the existence of a constant harmonic mean curvature foliation was established in the setting of a 3-dimensional asymptotically Schwarzschild manifold. Here, we generalize this construction to…

If $\Gamma$ is the nullity space of the curvature tensor of a Riemannian manifold $M^n$, it is well known that if its dimension is constant and if $M^n$ is complete then the distribution $\Gamma$ is completely integrable with flat leaves.…

We present a gravitational field theory that implements Horava's proposal of foliation-preserving-diffeomorphisms symmetry and higher spatial curvature directly in the canonical formalism. Due to the higher spatial derivative the theory is…

In this paper we present a rigidity theorem for locally isometric hypersurfaces with a curvature restriction in de Sitter space. This is an analogue to the case for Riemannian space forms given by Guan and Shen in [5].

With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K contact…

In this paper, we study $n$-dimensional complete minimal hypersurfaces in a hyperbolic space $H^{n+1}(-1)$ of constant curvature $-1$. We prove that a $3$-dimensional complete minimal hypersurface with constant scalar curvature in…

We prove that a H-surface M in H^2xR, |H| <= 1/2, inherits the symmetries of its boundary when the boundary is either a horizontal curve with curvature greater than one or two parallel horizontal curves with curvature greater than one,…

We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As applications, we prove a Bernstein theorem which says that if the image of the…

We investigate the structure of smooth holomorphic foliations with numerically flat tangent bundles on compact K\"ahler manifolds. Extending earlier results on non-uniruled projective manifolds by the second and fourth authors, we show that…

For a Riemannian manifold $M$, possibly with boundary, we consider the Riemannian product $M\times\mathbb{R}^k$ with a smooth positive function that weights the Riemannian measures. In this work we characterize parabolic hypersurfaces with…