scholarly journals The Energy Density Gap of Harmonic Maps between Finsler Manifolds

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Jingwei Han ◽  
Yao-yong Yu ◽  
Jing Yu
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Harmonic Maps ◽  
Finsler Manifold ◽  
Rigidity Theorem ◽  
Moving Frame ◽  
Finsler Manifolds ◽  
Variation Formula ◽  
Smooth Maps

We study the energy density function of nondegenerate smooth maps with vanishing tension field between two real Finsler manifolds. Firstly, we get a variation formula of energy density function by using moving frame. With this formula, we obtain a rigidity theorem of nondegenerate map with vanishing tension field from the Finsler manifold to the Berwald manifold.

Some rigidity theorems of harmonic maps between Finsler manifolds

2014 ◽  
Vol 25 (05) ◽  
pp. 1450043
Author(s):  
Qun He ◽  
Daxiao Zheng
Keyword(s):  
Riemannian Geometry ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Finsler Manifold ◽  
Finsler Manifolds ◽  
Rigidity Theorems

This paper is to study further properties of harmonic maps between Finsler manifolds. It is proved that any conformal harmonic map from an n(>2)-dimensional Finsler manifold to a Finsler manifold must be homothetic and some rigidity theorems for harmonic maps between Finsler manifolds are given, which improve some results in earlier papers and generalize Eells–Sampson's theorem and Sealey's theorem in Riemannian Geometry.

STABLE HARMONIC MAPS BETWEEN FINSLER MANIFOLDS AND SSU MANIFOLDS

2012 ◽  
Vol 14 (03) ◽  
pp. 1250015 ◽  
Author(s):  
JINTANG LI
Keyword(s):  
Harmonic Maps ◽  
Harmonic Map ◽  
American Mathematical Society ◽  
Variational Formula ◽  
Finsler Manifold ◽  
Finsler Manifolds ◽  
Recent Developments ◽  
Riemannian Case ◽  
The Stability ◽  
The Second Variation

Using the properties of Cartan tensor, we rewrite the second variation formula for harmonic maps between Finsler manifolds, and we prove that there is no non-degenerate stable harmonic map from a compact SSU manifold to any Finsler manifold, which is obtained by Howard and Wei for the Riemannian case. We also include a proof of a theorem of Shen–Wei which states that there is no non-degenerate stable harmonic map from a compact Finsler manifold to any SSU manifold, by the same second variational formula (see Eq. (2.1) in [Y. B. Shen and S. W. Wei, The stability of harmonic maps on Finster manifolds, Houston J. Math. 34 (2008) 1049–1056]) and the same method [S. W. Wei, An extrinsic average variational method, in Recent Developments in Geometry, Contemporary Mathematics, Vol. 101 (American Mathematical Society, Providence, RI, 1989), pp. 55–78].

An energy density function for papillary muscle encompassing both elastic and contractile properties

1981 ◽  
Vol 52 (5) ◽  
pp. 3674-3687 ◽  
Author(s):  
Willem Klip ◽  
Lloyd L. Hefner ◽  
Thomas C. Donald ◽  
David N. S. Reeves ◽  
Jane B. Hazelrig ◽  
...  
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Papillary Muscle ◽  
Contractile Properties

scholarly journals Geodesic Random Walks, Diffusion Processes and Brownian Motion on Finsler Manifolds

2021 ◽  
Author(s):  
Tianyu Ma ◽  
Vladimir S. Matveev ◽  
Ilya Pavlyukevich
Keyword(s):  
Brownian Motion ◽  
Diffusion Process ◽  
Random Walks ◽  
Diffusion Processes ◽  
Riemannian Metric ◽  
Finsler Manifold ◽  
Finsler Manifolds ◽  
Bounded Geometry ◽  
And Brownian Motion

AbstractWe show that geodesic random walks on a complete Finsler manifold of bounded geometry converge to a diffusion process which is, up to a drift, the Brownian motion corresponding to a Riemannian metric.

The strain energy density function

1986 ◽  
pp. 237-253
Author(s):  
G. C. Sih ◽  
J. G. Michopoulos ◽  
S. C. Chou
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Strain Energy Density Function

Conformal F-harmonic maps for Finsler manifolds

2014 ◽  
Vol 134 (2) ◽  
pp. 227-234
Author(s):  
Jintang Li
Keyword(s):  
Harmonic Maps ◽  
Finsler Manifolds

Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio

2019 ◽  
Vol 25 (2) ◽  
pp. 348-361 ◽  
Author(s):  
Zhenyu Liu ◽  
Han Liu ◽  
Guifang Duan ◽  
Jianrong Tan
Keyword(s):  
Energy Density ◽  
Modeling And Simulation ◽  
Density Function ◽  
Thickness Ratio ◽  
Equivalent Transformation ◽  
Deformation Model ◽  
Bilayer Structure ◽  
Bending Deformation ◽  
Stretching Deformation ◽  
Deformation Models

This paper addresses the problem of deformation modeling and simulation of 4D printed polymeric bilayer structures considering the thickness ratio. Through an equivalent transformation, the folding deformation model is transformed into two simpler deformation models, stretching and bending, which greatly reduces the complexity of the modeling problem. The stretching deformation model is developed by Hooke’s law, and based on the final strain of the stretching deformation, which is determined by the thickness ratio, a new hyperelastic energy density function considering the thickness ratio is defined to calculate the energy of the bilayer structure during the bending deformation. According to the new energy density function, the bending deformation model considering the thickness ratio is developed by minimizing the energy of the bilayer structure during the bending deformation. Numerical simulations show encouraging results obtained by the proposed model.

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