Microflexiblity and local integrability of horizontal curves

Alvaro del Pino, Tobias Shin

Research output: Contribution to journalArticleAcademicpeer-review


Let (Formula presented.) be an analytic bracket-generating distribution. We show that the subspace of germs that are singular (in the sense of control theory) has infinite codimension within the space of germs of smooth curves tangent to (Formula presented.). We formalize this as an asymptotic statement about finite jets of tangent curves. This solves, in the analytic setting, a conjecture of Eliashberg and Mishachev regarding an earlier claim by Gromov about the microflexibility of the tangency condition. From these statements it follows, by an argument due to Gromov, that the (Formula presented.) -principle holds for maps and immersions transverse to (Formula presented.).

Original languageEnglish
Number of pages36
JournalMathematische Nachrichten
Publication statusE-pub ahead of print - 16 Jun 2024


  • Curves
  • Endpoint map
  • H-principle
  • Horizontal
  • Singular curves
  • Tangent distributions


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