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.

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.

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.

HELICOIDAL SURFACES WITH PRESCRIBED CURVATURES IN Nil3

2013 ◽  
Vol 24 (14) ◽  
pp. 1350107 ◽  
Author(s):  
DAE WON YOON ◽  
DONG-SOO KIM ◽  
YOUNG HO KIM ◽  
JAE WON LEE
Keyword(s):  
Heisenberg Group ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Smooth Functions ◽  
Constant Gaussian Curvature ◽  
3 Dimensional ◽  
Helicoidal Surfaces ◽  
Prescribed Gaussian Curvature

In the present paper, we study helicoidal surfaces in the 3-dimensional Heisenberg group Nil3. Also, we construct helicoidal surfaces in Nil3 with prescribed Gaussian curvature or mean curvature given by smooth functions. As the results, we classify helicoidal surfaces with constant Gaussian curvature or constant mean curvature.

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.

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