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Inventiones mathematicae

, Volume 206, Issue 3, pp 693–704 | Cite as

Non-minimality of corners in subriemannian geometry

  • Eero Hakavuori
  • Enrico Le DonneEmail author
Article

Abstract

We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev’s list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.

Mathematics Subject Classification

53C17 49K21 28A75 

Notes

Acknowledgments

The authors thank A. Ottazzi, D. Vittone, and the anonymous referees for their helpful remarks. E.L.D. acknowledges the support of the Academy of Finland project no. 288501.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland

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