scholarly journals The Weighted Mean Curvature Derivative of a Space-Filling Diagram

2020 ◽  
Vol 8 (1) ◽  
pp. 51-67
Author(s):  
Arsenyi Akopyan ◽  
Herbert Edelsbrunner
Keyword(s):  
Free Energy ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Solid Sphere ◽  
Solvation Free Energy ◽  
Dimensional Euclidean Space ◽  
Space Filling ◽  
Weighted Mean ◽  
3 Dimensional ◽  
Weighted Mean Curvature

AbstractRepresenting an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.

scholarly journals The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram

2020 ◽  
Vol 8 (1) ◽  
pp. 74-88
Author(s):  
Arsenyi Akopyan ◽  
Herbert Edelsbrunner
Keyword(s):  
Free Energy ◽  
Linear Combination ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Solvation Free Energy ◽  
Space Filling ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Derivatives Of

AbstractThe morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.

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.

scholarly journals Constructions of Helicoidal Surfaces in a 3-Dimensional Complete Manifold with Density

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 27
Author(s):  
Önder Yıldız
Keyword(s):  
Mean Curvature ◽  
Extrinsic Curvature ◽  
Positive Density ◽  
Complete Manifold ◽  
Weighted Mean ◽  
3 Dimensional ◽  
Weighted Mean Curvature ◽  
Helicoidal Surfaces ◽  
Helicoidal Surface ◽  
Manifold With Density

In this paper, we construct a helicoidal surface with a prescribed weighted mean curvature and weighted extrinsic curvature in a 3-dimensional complete manifold with a positive density function. We get a result for the minimal case. Additionally, we give examples of a helicoidal surface with a weighted mean curvature and weighted extrinsic curvature.

scholarly journals Type I+ Helicoidal Surfaces with Prescribed Weighted Mean or Gaussian Curvature in Minkowski Space with Density

2018 ◽  
Vol 26 (3) ◽  
pp. 99-108 ◽  
Author(s):  
Önder Gökmen Yıldız ◽  
Selman Hızal ◽  
Mahmut Akyiğit
Keyword(s):  
Minkowski Space ◽  
Density Function ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Positive Density ◽  
Type I ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Helicoidal Surfaces ◽  
Helicoidal Surface

AbstractIn this paper, we construct a helicoidal surface of type I+ with prescribed weighted mean curvature and Gaussian curvature in the Minkowski 3−space ${\Bbb R}_1^3$with a positive density function. We get a result for minimal case. Also, we give examples of a helicoidal surface with weighted mean curvature and Gaussian curvature.

Rigidity of entire graphs in weighted product spaces with nonnegative Bakry–Émery–Ricci tensor

2017 ◽  
Vol 17 (1) ◽  
Author(s):  
Henrique F. de Lima ◽  
Arlandson M. S. Oliveira ◽  
Márcio S. Santos
Keyword(s):  
Smooth Function ◽  
Mean Curvature ◽  
Ricci Tensor ◽  
Product Space ◽  
Product Spaces ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Entire Graphs

AbstractWe study the rigidity of entire graphs defined over the fiber of a weighted product space whose Bakry–Émery–Ricci tensor is nonnegative. Supposing that the weighted mean curvature is constant and assuming appropriated constraints on the norm of the gradient of the smooth function

scholarly journals Hopf-type theorem for self-shrinkers

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hilário Alencar ◽  
Gregório Silva Neto ◽  
Detang Zhou
Keyword(s):  
Fundamental Form ◽  
Mean Curvature ◽  
Type Theorem ◽  
Complex Function ◽  
Curvature Vector ◽  
Second Fundamental Form ◽  
Dimensional Euclidean Space ◽  
Position Vector ◽  
Weighted Mean Curvature ◽  
Radial Weight

Abstract In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three-dimensional Euclidean space ℝ 3 {{\mathbb{R}}^{3}} is a round sphere, provided its mean curvature and the norm of the its position vector have an upper bound in terms of the norm of its traceless second fundamental form. The example constructed by Drugan justifies that the hypothesis on the second fundamental form is necessary. We can also prove the same kind of rigidity results for surfaces with parallel weighted mean curvature vector in ℝ n {{\mathbb{R}}^{n}} with radial weight. These results are applications of a new generalization of Cauchy’s Theorem in complex analysis which concludes that a complex function is identically zero or its zeroes are isolated if it satisfies some weak holomorphy.

Comparison theorems on smooth metric measure spaces with boundary

2016 ◽  
Vol 16 (4) ◽  
Author(s):  
Lin Feng Wang ◽  
Ze Yu Zhang ◽  
Yu Jie Zhou
Keyword(s):  
Mean Curvature ◽  
Comparison Theorems ◽  
Metric Measure Spaces ◽  
Weighted Mean ◽  
Dirichlet Eigenvalue ◽  
Weighted Mean Curvature ◽  
First Dirichlet Eigenvalue ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces ◽  
Weighted Laplacian

AbstractIn this paper we study smooth metric measure spaces with boundary via the Bakry–Émery curvature and the weighted mean curvature of the boundary. We establish the weighted Laplacian comparison theorems and the upper bound estimates of the distance from any point of the manifold to its boundary. As applications, we derive lower bound estimates for the first Dirichlet eigenvalue.

Sign in / Sign up

Export Citation Format

Share Document