In this paper, we prove a general halfspace theorem for constant mean curvature surfaces. Under certain hypotheses, we prove that, in an ambient space M, any constant mean curvature H0 surface on one side of a constant mean curvature H0 surface Σ0 is an equidistant surface to Σ0. The main hypotheses of the theorem are that Σ0 is parabolic and the mean curvature of the equidistant surfaces to Σ0...

the price of single point diamond tools with a sharp tip is very high due to complex machining process and highly expensive machining equipments. yet, the performance is not quite satisfactory. in this paper, we have presented a very simple and cost effective machining process for the sharpening and polishing of diamond stylus using low energy reactive ion beam machining (ribm). in our method, ...

In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G3. Also, we classify linear Weingarten rotational surfaces in G3. A linear Weingarten surface is the surface having a linear equation between the Gaussian curvature and the mean curvature of a surface. In last section, we construct isotropic rotational surfaces in G3 with prescribed mean curvature...

Surface creases provide us with important information about the shapes of objects and can be intuitively defined as curves on a surface along which the surface bends sharply. Our mathematical description of such surface creases is based on study of extrema of the principal curvatures along their curvature lines. On a smooth generic surface we define ridges to be the local positive maxima of the...

The price of single point diamond tools with a sharp tip is very high due to complex machining process and highly expensive machining equipments. Yet, the performance is not quite satisfactory. In this paper, we have presented a very simple and cost effective machining process for the sharpening and polishing of diamond stylus using low energy reactive ion beam machining (RIBM). In our method, ...

Simultaneous contrast effects have been found across a wide range of visual dimensions. We describe a simultaneous contrast effect--three-dimensional curvature contrast--in which the apparent curvature of a surface defined by shading and texture information is influenced by the curvature of a surrounding surface. The effect is strong and easily measurable. We asked whether the effect depends up...

In this note we consider asymptotically flat manifolds with non-negative scalar curvature and an inner boundary which is an outermost minimal surface. We show that there exists an upper bound on the mean curvature of a constant mean curvature surface homologous to a subset of the interior boundary components. This bound allows us to find a maximizer for the constant mean curvature of a surface ...

We are exploring new methods of spike detection to improve spike-sorting in tetrode recordings. Based on our observation that the four channels of the tetrode carry highly correlated signals, we propose the use of a hyperellipsoidal thresholding surface in the 4-dimensional space of the signal values to detect spikes. This surface is determined by the cross-channel covariance matrix and provide...

3 is the boundary of two spherical caps of constant mean curvature H for any positive number H, which is at most the radius of C. It is natural to ask whether spherical caps are the only possible examples. Some examples of constant mean curvature immersed tori by Wente [7] indicate that there are compact genus-one immersed constant mean curvature surfaces with boundary C that are approximated b...

While there is a rich literature on methods for computing the curvature of discrete surfaces, the case of discrete surfaces with boundary is often ignored. We show how to compute curvature measures for discrete surfaces with boundary using the theory of normal cycles. Our curvature formulae for discrete surfaces exhibit boundary terms not seen in previous formulae. We also derive error bounds c...