TY - JOUR

T1 - On the geometric structure of currents tangent to smooth distributions

AU - Alberti, Giovanni

AU - Massaccesi, Annalisa

AU - Stepanov, Eugene

N1 - Giovanni Alberti. Annalisa Massaccesi. Eugene Stepanov. "On the geometric structure of currents tangent to smooth distributions." J. Differential Geom. 122 (1) 1 - 33, September 2022. https://doi.org/10.4310/jdg/1668186786

PY - 2022

Y1 - 2022

N2 - It is well known that a kk-dimensional smooth surface in a Euclidean space cannot be tangent to a non-involutive distribution of kk-dimensional planes. In this paper we discuss the extension of this statement to weaker notions of surfaces, namely integral and normal currents. We find out that integral currents behave to this regard exactly as smooth surfaces, while the behavior of normal currents is rather multifaceted. This issue is strictly related to a geometric property of the boundary of currents, which is also discussed in details.

AB - It is well known that a kk-dimensional smooth surface in a Euclidean space cannot be tangent to a non-involutive distribution of kk-dimensional planes. In this paper we discuss the extension of this statement to weaker notions of surfaces, namely integral and normal currents. We find out that integral currents behave to this regard exactly as smooth surfaces, while the behavior of normal currents is rather multifaceted. This issue is strictly related to a geometric property of the boundary of currents, which is also discussed in details.

UR - https://projecteuclid.org/journals/journal-of-differential-geometry/volume-122/issue-1/On-the-geometric-structure-of-currents-tangent-to-smooth-distributions/10.4310/jdg/1668186786.xml

M3 - Article

VL - 122

SP - 1

EP - 33

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 1

ER -