TY - JOUR

T1 - A rough calculus approach to level sets in the Heisenberg group

AU - Magnani, Valentino

AU - Stepanov, Eugene

AU - Trevisan, Dario

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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 R2. 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.

AB - 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 R2. 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.

KW - 26A42 (secondary)

KW - 28A75 (primary)

KW - 53C17

UR - http://www.scopus.com/inward/record.url?scp=85044499225&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/rough-calculus-approach-level-sets-heisenberg-group

U2 - 10.1112/jlms.12115

DO - 10.1112/jlms.12115

M3 - Article

AN - SCOPUS:85044499225

VL - 97

SP - 495

EP - 522

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 3

ER -