Published January 31, 2025 | Version v1
Publication

Not all sub-Riemannian minimizing geodesics are smooth

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Description

A longstanding open question in sub-Riemannian geometry is the following: are sub-Riemannian length minimizers smooth? We give a negative answer to this question, exhibiting an example of a C 2 but not C 3 length-minimizer of a real-analytic (even polynomial) sub-Riemannian structure.

Additional details

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URL
https://ensta-paris.hal.science/hal-04885315
URN
urn:oai:HAL:hal-04885315v2

Origin repository

Origin repository
UNICA