Area of intrinsic graphs and coarea formula in Carnot groups
Julia, A., Nicolussi Golo, S., & Vittone, D. (2022). Area of intrinsic graphs and coarea formula in Carnot groups. Mathematische Zeitschrift, 301(2), 1369-1406. https://doi.org/10.1007/s00209-021-02916-2
Published inMathematische Zeitschrift
© The Author(s) 2022
We consider submanifolds of sub-Riemannian Carnot groups with intrinsic C1 regularity (C1H). Our first main result is an area formula for C1H intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on rectifiable sets. Our second main result is a coarea formula for slicing C1H submanifolds into level sets of a C1H function.
PublisherSpringer Science and Business Media LLC
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Additional information about fundingThe authors are supported by the University of Padova STARS Project “Sub-Riemannian Geometry and Geometric Measure Theory Issues: Old and New” (SUGGESTION). They also acknowledge the support of GNAMPA of INdAM and FFABR 2017 of MIUR (Italy). Open Access funding provided by University of Jyväskylä (JYU).
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