نتایج جستجو برای: gauss curvature

تعداد نتایج: 52200  

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

Journal: :Annals of the Alexandru Ioan Cuza University - Mathematics 2021

We construct a concrete example of constant Gauss curvature $K = 1$ on the 2-sphere having all geodesics closed and same length.

2005
GIL SOLANES

We give an integral-geometric proof of the Gauss-Bonnet theorem for hypersurfaces in constant curvature spaces. As a tool, we obtain variation formulas in integral geometry with interest in its own.

Journal: :Journal of Nanobiotechnology 2006
Yajun Yin Jie Yin

On the basis of the integral theorems about the mean curvature and Gauss curvature, geometric conservation laws for cells or vesicles are proved. These conservation laws may depict various special bionano structures discovered in experiments, such as the membrane nanotubes and singular points grown from the surfaces of cells or vesicles. Potential applications of the conservation laws to lipid ...

2007
S. Deser Bayram Tekin

We propose a novel but natural definition of conserved quantities for gravity models quadratic and higher in curvature. Based on the spatial asymptotics of curvature rather than of metric, it avoids the GR energy machinery’s more egregious problems–such as zero energy “theorems” and failure in flat backgrounds – in this fourth-derivative realm. In D > 4, the present expression indeed correctly ...

2006
ALEXANDRE GONÇALVES KAREN UHLENBECK

The study of constant mean curvature surfaces in a space-form has been an active field since the work of H. Hopf in the 1920’s and H.Liebmann in the years around 1900. The questions which are generally of interest are global questions of existence and uniqueness in complete 3-manifolds. We deal in this short paper on a question of existence and uniqueness with respect to the complex structure a...

Journal: :Proceedings of the National Academy of Sciences of the United States of America 2008
Ashkan Vaziri L Mahadevan

The dried raisin, the crushed soda can, and the collapsed bicycle inner tube exemplify the nonlinear mechanical response of naturally curved elastic surfaces with different intrinsic curvatures to a variety of different external loads. To understand the formation and evolution of these features in a minimal setting, we consider a simple assay: the response of curved surfaces to point indentatio...

1996
XU-JIA WANG

Let f(x) be a given positive function in Rn+1. In this paper we consider the existence of convex, closed hypersurfaces X so that its GaussKronecker curvature at x ∈ X is equal to f(x). This problem has variational structure and the existence of stable solutions has been discussed by Tso (J. Diff. Geom. 34 (1991), 389–410). Using the Mountain Pass Lemma and the Gauss curvature flow we prove the ...

2009
MICHAEL T. ANDERSON MARCUS A. KHURI

We prove the existence of asymptotically flat solutions to the static vacuum Einstein equations on M = R \B with prescribed metric γ and mean curvature H on ∂M ≃ S, provided H > 0 and H has no critical points where the Gauss curvature Kγ ≤ 0. This gives a partial resolution of a conjecture of Bartnik on such static vacuum extensions. The existence and uniqueness of such extensions is closely re...

نمودار تعداد نتایج جستجو در هر سال

با کلیک روی نمودار نتایج را به سال انتشار فیلتر کنید