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A rough calculus approach to level sets in the Heisenberg group
Author(s) -
Magnani Valentino,
Stepanov Eugene,
Trevisan Dario
Publication year - 2018
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12115
Subject(s) - mathematics , heisenberg group , group (periodic table) , measure (data warehouse) , calculus (dental) , ode , pure mathematics , mathematical analysis , computer science , medicine , dentistry , chemistry , organic chemistry , database
We introduce novel equations, in the spirit of rough path theory, that parametrize level sets of intrinsically regular maps on the Heisenberg group with values in R 2 . These equations can be seen as a sub‐Riemannian counterpart to classical ODEs arising from the implicit function theorem. We show that they enjoy all the natural well‐posedness properties, thus allowing for a ‘good calculus’ on nonsmooth level sets. We apply these results to prove an area formula for the intrinsic measure of level sets, along with the corresponding coarea formula.