Differential inequalities on Finsler manifolds and their geometric applications

Jiang, Qi; Zhang, Fu-e

doi:10.1016/j.jmaa.2019.01.075

Journal of Mathematical Analysis and Applications

2019

DOI: 10.1016/j.jmaa.2019.01.075

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Differential inequalities on Finsler manifolds and their geometric applications

Qi Jiang

Fu-e Zhang

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2022

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The Dynamics of Deforming Manifold: A Mathematical Model

Zhuang

Mastorakis

2022

International Journal of Mathematical Models and Methods in Applied Sciences

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In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have clear physical meanings. The proposed model is a modification of the general differential dynamic model, with constraints of spatial and temporal continuity on the deforming field. The deformation integral and derivative are presented as compact expressions of manifold deforming process. Moreover, a specific autonomous deforming field with flattening effect is defined, which provides a novel geometric viewpoint on data dimension reduction. The effectiveness of this autonomous deforming field is proved by numerical computation simulations, which indicate the promising potential of the proposed model in practical dimension reduction tasks.

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The Dynamics of Deforming Manifold: A Mathematical Model

Zhuang

Mastorakis

2022

International Journal of Mathematical Models and Methods in Applied Sciences

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Differential inequalities on Finsler manifolds and their geometric applications

Cited by 1 publication

References 15 publications

The Dynamics of Deforming Manifold: A Mathematical Model

The Dynamics of Deforming Manifold: A Mathematical Model

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