Weighted minimal affine translation surfaces in Euclidean space with density

2018 ◽  
Vol 15 (11) ◽  
pp. 1850196 ◽  
Author(s):  
Dae Won Yoon ◽  
Zühal Küçükarslan Yüzbaşı
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Translation Surfaces ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Surfaces In Euclidean Space ◽  
Affine Translation

The aim of this work is to study affine translation surfaces in the Euclidean 3-space with density. We completely classify affine translation surfaces with zero weighted 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.

Weighted minimal translation surfaces in Minkowski 3-space with density

2017 ◽  
Vol 14 (12) ◽  
pp. 1750178 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Mean Curvature ◽  
Second Order ◽  
Translation Surfaces ◽  
Weighted Mean ◽  
Smooth Functions ◽  
Weighted Mean Curvature ◽  
Straight Line ◽  
Non Linear ◽  
Linear Ode

The aim of this work is to study translation surfaces in a Minkowski 3-space [Formula: see text] with density. Translation surfaces in [Formula: see text] are defined as the two generating curves which lie in orthogonal planes. They have actually three different possible parametrizations according to the intersecting straight line of the two planes. We completely classify all translation surfaces with zero weighted mean curvature in [Formula: see text] with density [Formula: see text] by solving the second-order non-linear ODE with some smooth functions.

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 Construction of constant mean curvature n-noids using the DPW method

2020 ◽  
Vol 2020 (763) ◽  
pp. 223-249 ◽  
Author(s):  
Martin Traizet
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Genus Zero ◽  
Constant Mean Curvature Surfaces ◽  
Surfaces In Euclidean Space

AbstractWe construct constant mean curvature surfaces in euclidean space with genus zero and n ends asymptotic to Delaunay surfaces using the DPW method.

Minimal Translation Surfaces in Euclidean Space

2017 ◽  
Vol 27 (4) ◽  
pp. 2926-2937 ◽  
Author(s):  
Rafael López ◽  
Óscar Perdomo
Keyword(s):  
Euclidean Space ◽  
Translation Surfaces ◽  
Surfaces In Euclidean Space

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.

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