Hodge Theory on Metric Spaces

被引：0
作者：
Laurent Bartholdi
Thomas Schick
Nat Smale
Steve Smale
机构：
[1] Georg-August-Universität,
[2] University of Utah,undefined
[3] City University of Hong Kong,undefined
来源：
Foundations of Computational Mathematics | 2012年 / 12卷
关键词：
Hodge theory; cohomology; Metric spaces; Harmonic forms; Medium-scale geometry; 58A14; 54E05; 55P55; 57M50;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Hodge theory is a beautiful synthesis of geometry, topology, and analysis which has been developed in the setting of Riemannian manifolds. However, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step toward understanding the geometry of vision.
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页码：1 / 48
页数：47
相关论文
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