Related papers: Extrinsic radius pinching for hypersurfaces of spa…

We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.

We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition we prove that the…

We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.

We generalize the spinorial characterization of isometric immersions of surfaces in R^3 given by T. Friedrich (On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998)) to surfaces in S^3 and H^3. The main…

We consider hypersurfaces in the real Euclidean space $\mathbb{R}^{n+1}$ ($n\geq2$) which are relatively normalized. We give necessary and sufficient conditions a) for a surface of negative Gaussian curvature in $\mathbb{R}^3$ to be ruled,…

The paper is centered around a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert-Einstein functional on the space of "warped polyhedra" with a fixed metric on the…

In this work we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and apply it to investigate conditions for the leaves…

In this paper we address the problem of studying those complex manifolds $M$ equipped with extremal metrics $g$ induced by finite or infinite dimensional complex space forms. We prove that when $g$ is assumed to be radial and the ambient…

We consider a compact submanifold $M$ of a Riemannian manifold $N$ and we use the second variation formula as a tool to drive some geometric results on reach$(M, N)$ the reach of $M$ in $N$, including some useful relations between the…

We analyze a model of hypercubic random surfaces with an extrinsic curvature term in the action. We find a first order phase transition at finite coupling separating a branched polymer from a stable flat phase.

Let $M$ be a closed hyperbolic $3$-manifold. A homotopy class $[S]$ of surfaces in $M$ is filling if any representative cuts $M$ into components contractible in $M$. We prove that there exist $\epsilon_0, g_0>0$ such that every homotopy…

We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in 3-dimensional space forms.

In this paper, we prove a local rigidity of convex hypersurfaces in the spaces of constant curvature of dimension $n\ge4$. Namely, we show that two convex isometric hypersurfaces are congruent locally around their corresponding under the…

Nontrivial infinitesimal bendings for a class of two-dimensional surfaces are constructed. The surfaces considered here are orientable; compact; with boundary; have positive curvature everywhere except at finitely many planar points; and…

The problem of possible astrophysical consequences of the existence of exotic differential structures on manifolds is discussed. It is argued that corrections to the curvature of the form of a source like terms should be expected in the…

We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.

We prove that a generic area-preserving diffeomorphism of a compact surface with non-empty boundary has an equidistributed set of periodic orbits. This implies that such a diffeomorphism has a dense set of periodic points, although we also…

We show that a locally Ahlfors 2-regular and locally linearly locally contractible metric surface is locally quasisymmetrically equivalent to the disk. We also discuss an application of this result to the problem of characterizing surfaces…

In this paper we use the notion of stability for free boundary surfaces with constant higher order mean curvature to obtain rigidity results for $H_2$-surfaces with free boundary of a geodesic ball of a simply connected $3$-dimensional…

It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never…