We derive local integral and supestimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situations of physical interest, such as dynamical horizons.

A Ricci surface is a Riemannian 2-manifold (M, g) whose Gaussian curvature K satisfies K∆K+g(dK, dK)+4K = 0. Every minimal surface isometrically embedded in R is a Ricci surface of non-positive curvature. At the end of the 19 century Ricci-Curbastro has proved that conversely, every point x of a Ricci surface has a neighborhood which embeds isometrically in R as a minimal surface, provided K(x)...

A structured light system provides a dense sampling of 3D coordinates from visible surfaces in a scene. This paper compares several methods for determining the principle frame, Gaussian curvature, and mean curvature at each visible surface point from this data. The principle frame, etc, parameterize a model which completely characterizes the local surface geometry. Given the local surface model...

We will study a surface in R without any umbilical point such that the integral curves of some principal distribution are geodesics. In particular, the lines of curvature of such a surface will be characterized intrinsically and extrinsically: the semisurface structure of such a surface will be characterized in terms of local representation of the first fundamental form; the curvatures and the ...

The mathematicians for centuries have researched the surfaces theory. In this paper, we consider strophoidal surface in three dimensional Euclidean space E^3. We present notations of a geometry. addition, stating helicoidal surface, define and calculate its Gauss map, Gaussian curvature, mean curvature. Finally, give some relations curvature that kind surfaces.

During the development of subdivision surface methods one of the important questions has been the degree of continuity of the limit surface. In particular whether continuity of curvature can be achieved at the extraordinary points. However, there are several different curvature behaviours, not just two, and this note demonstrates them by examples. q 2003 Elsevier Science Ltd. All rights reserved.

In this paper we study surfaces in Euclidean 3-space foliated by pieces of circles and that satisfy a Weingarten condition of type aH+bK = c, where a, b and c are constant and H and K denote the mean curvature and the Gauss curvature respectively. We prove that a such surface must be a surface of revolution, a Riemann minimal surface or a generalized cone.

A linear Weingarten surface in Euclidean space R 3 is a surface whose mean curvature H and Gaussian curvature K satisfy a relation of the form aH + bK = c, where a, b, c ∈ R. Such a surface is said to be hyperbolic when a + 4bc < 0. In this paper we classify all rotational linear Weingarten surfaces of hyperbolic type. As a consequence, we obtain a family of complete hyperbolic linear Weingarte...

In many applications it is required to have a curvature-dependent surface sampling, based on a local shape analysis. In this work we show how this can be achieved by using the support function (SF) representation of a surface. This representation, a classical tool in Convex Geometry, has been recently considered in CAD problems for computing surface offsets and for analyzing curvatures. Startin...

This paper presents empirical support for a new observer model of inferring three-dimensional shape from monocular texture cues. By measuring observers' abilities to estimate the relative three-dimensional curvature along a textured surface from two-dimensional projected images, and concurrently examining the local spectral changes occurring in the projected image for various texture patterns, ...