A nonlinear inequality involving the mean curvature of a spacelike surface in 3-dimensional GRW spacetimes and Calabi-Bernstein type problems

2016 ◽  
pp. 141-152 ◽  
Author(s):  
Alfonso Romero ◽  
Rafael Rubio
Keyword(s):  
Mean Curvature ◽  
Spacelike Surface ◽  
Bernstein Type ◽  
3 Dimensional ◽  
Nonlinear Inequality ◽  
The Mean

scholarly journals On the second Gaussian curvature of ruled surfaces in Euclidean $3$-space

2006 ◽  
Vol 37 (3) ◽  
pp. 221-226 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Euclidean Space ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
The Mean ◽  
Second Gaussian Curvature

In this paper, we mainly investigate non developable ruled surface in a 3-dimensional Euclidean space satisfying the equation $K_{II} = KH$ along each ruling, where $K$ is the Gaussian curvature, $H$ is the mean curvature and $K_{II}$ is the second Gaussian curvature.

COMPLETE CMC SPACELIKE SURFACES WITH BOUNDED HYPERBOLIC ANGLE IN GENERALIZED ROBERTSON–WALKER SPACETIMES

2010 ◽  
Vol 07 (06) ◽  
pp. 961-978 ◽  
Author(s):  
MAGDALENA CABALLERO ◽  
ALFONSO ROMERO ◽  
RAFAEL M. RUBIO
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Existence Theorems ◽  
Natural Extension ◽  
Minkowski Spacetime ◽  
Spacelike Surface ◽  
3 Dimensional ◽  
Spacelike Surfaces ◽  
Hyperbolic Angle ◽  
Wide Family

Complete spacelike surfaces with constant mean curvature (CMC) and bounded hyperbolic angle in Generalized Robertson–Walker (GRW) spacetimes, obeying certain natural curvature assumptions, are studied. This boundedness assumption arises as a natural extension of the notion of bounded hyperbolic image of a spacelike surface in the 3-dimensional Lorentz–Minkowski spacetime. The results obtained apply to complete CMC spacelike surfaces lying between two spacelike slices in an GRW spacetime, in the steady state spacetime and in a static GRW spacetime. As an application, uniqueness and non-existence theorems for certain CMC spacelike surface differential equations in a wide family of open GRW spacetimes are given.

scholarly journals On Bernstein-Type Theorems in Semi-Riemannian Warped Products

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Mean Curvature ◽  
Warped Products ◽  
Bernstein Type ◽  
Complete Spacelike Hypersurfaces ◽  
Spacelike Hypersurfaces ◽  
The Mean

Complete spacelike hypersurfaces immersed in semi-Riemannian warped products are investigated. By using a technique according to Yau (1976) and a reasonable restriction on the mean curvature of the hypersurfaces, we obtain some new Bernstein-type theorems which extend some known results proved by Camargo et al. (2011) and Colares and Lima (2012).

scholarly journals Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow

2020 ◽  
Vol 18 (1) ◽  
pp. 1518-1530
Author(s):  
Xuesen Qi ◽  
Ximin Liu
Keyword(s):  
Laplace Operator ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Second Fundamental Form ◽  
Coefficient Function ◽  
First Eigenvalue ◽  
Initial Hypersurface ◽  
The Mean ◽  
The Laplace Operator

Abstract In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF). By imposing conditions associated with the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced MCF, and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao’s work. Moreover, we give an example to specify applications of conclusions obtained above.

scholarly journals Comparison of Bite Force in Patients After Treatment of Mandibular Fractures With 3-Dimensional Locking Miniplate and Standard Miniplates

2019 ◽  
Vol 1 (1) ◽  
pp. 7-10
Author(s):  
Gaurav Singh ◽  
Madan Mishra ◽  
Amit Gaur ◽  
Dhritiman Pathak
Keyword(s):  
Treatment Strategies ◽  
Bite Force ◽  
Mandibular Fractures ◽  
Time Intervals ◽  
Experimental Conditions ◽  
3 Dimensional ◽  
The Mean ◽  
Group 2 ◽  
Drilling Conditions ◽  
Group 1

Background: Fractures of the mandible can be studied and described in anatomic terms, functional considerations, treatment strategies, and outcome measures. The performance of any fixation system depends on multiple factors including plate adaptation, screw placement, bone quality, drilling conditions, and postoperative patient compliance. Bite force assesses masticatory muscle function under clinical and experimental conditions. Method: 30 patients with isolated, noncomminuted mandibular fractures were randomly divided into two equal groups. Group 1 patients were treated using 3-dimensional locking miniplates and group 2 patients were treated with standard miniplates. The bite forces were recorded at definite time intervals: preoperatively, and second week, sixth week, third month, and sixth month postoperatively. Result: At 6 weeks postoperative, 3 month postoperative, and 6 month postoperative, the mean bite force was found to be significantly higher among group 1 patients as compared to those in group 2 in all the sites. While at 2 week postoperative, the mean bite force was found to be significantly higher in Group 2 as compared to Group 1 at incisor region. Conclusion: The overall results of the present study show better performance in bite force for the 3-dimensional locking miniplate when compared with standard miniplates.

The focusing of radiation by a random surface when the source is at a finite distance

1960 ◽  
Vol 56 (1) ◽  
pp. 27-40 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Mean Curvature ◽  
Joint Distribution ◽  
Total Curvature ◽  
Statistical Distribution ◽  
Constant Parameter ◽  
Random Surface ◽  
Second Derivatives ◽  
Finite Distance ◽  
The Mean ◽  
Image Position

Imagine a nearly horizontal, statistically uniform, random surface ζ(x, y), Gaussian in the sense that the second derivatives , , have a normal joint distribution. The problem considered is the statistical distribution of the quantitywhere J and Ω denote the mean curvature and total curvature of the surface, respectively, and ν is a constant parameter.

Sign in / Sign up

Export Citation Format

Share Document