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 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 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

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.

scholarly journals Weighted minimal translation surfaces in the Galilean space with density

2017 ◽  
Vol 15 (1) ◽  
pp. 459-466 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Mean Curvature ◽  
Linear Density ◽  
Translation Surface ◽  
Plane Curves ◽  
Isotropic Plane ◽  
Translation Surfaces ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Galilean Space ◽  
Log Linear

Abstract Translation surfaces in the Galilean 3-space G3 have two types according to the isotropic and non-isotropic plane curves. In this paper, we study a translation surface in G3 with a log-linear density and classify such a surface with vanishing weighted mean curvature.

scholarly journals Volume Growth of Complete Submanifolds in Gradient Ricci Solitons with Bounded Weighted Mean Curvature

2019 ◽  
Author(s):  
Xu Cheng ◽  
Matheus Vieira ◽  
Detang Zhou
Keyword(s):  
Mean Curvature ◽  
Volume Growth ◽  
Curvature Vector ◽  
Ricci Soliton ◽  
Weighted Mean ◽  
Bounded Geometry ◽  
Gradient Ricci Solitons ◽  
Ambient Manifold ◽  
Complete Submanifolds ◽  
Weighted Mean Curvature

Abstract In this article, we study properly immersed complete noncompact submanifolds in a complete shrinking gradient Ricci soliton with weighted mean curvature vector bounded in norm. We prove that such a submanifold must have polynomial volume growth under some mild assumption on the potential function. On the other hand, if the ambient manifold is of bounded geometry, we prove that such a submanifold must have at least linear volume growth. In particular, we show that a properly immersed complete noncompact hypersurface in the Euclidean space with bounded Gaussian weighted mean curvature must have polynomial volume growth and at least linear volume growth.

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