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arXiv · 1803.10485

Partial regularity of minimizers for real-analytic sub-Riemannian metrics

Paolo Albano·Antonio Bove
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Abstract

In the real-analytic setting, we show that all sub-Riemannian minimizers (parametrized by the arc-length) are real-analytic everywhere except an at most countable non-dense set. In particular, non-analyticity may occur only on a set of measure zero of the domain of definition of a sub-Riemannian minimizer. Furthermore, we provide a geometrical condition which implies the absence of the so called strictly abnormal minimizers. In particular, under such condition, all sub-Riemannian minimizers (parametrized by the arc-length) are real-analytic.

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Paolo Albano, Antonio Bove. 2018-03-28. Partial regularity of minimizers for real-analytic sub-Riemannian metrics. https://arxiv.org/abs/1803.10485

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