Bigolin, Francesco; Serra Cassano, Francesco Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs. (English) Zbl 1188.53027 Adv. Calc. Var. 3, No. 1, 69-97 (2010). The authors consider \(\mathbb H\)-regular graphs, a class of intrinsic regular hypersurfaces in the Heisenberg group \({\mathbb H}^n={\mathbb C}^n\times {\mathbb R}\) endowed with a left invariant metric \(d_\infty\) equivalent to its Carnot Caratheodory metric. They obtain the following geometric properties: a uniqueness result for \(\mathbb H\)-regular graphs of prescribed horizontal normal as well as their regularity as long as there is regularity on the horizontal normal. These results contribute to the study of further geometric properties of this class graph. Reviewer: Peibiao Zhao (Nanjing) Cited in 1 ReviewCited in 20 Documents MSC: 53C17 Sub-Riemannian geometry 35L60 First-order nonlinear hyperbolic equations 49Q15 Geometric measure and integration theory, integral and normal currents in optimization Keywords:Heisenberg group; Carnot-Caratheodory metric; intrinsic graph; nonlinear first-order PDEs PDFBibTeX XMLCite \textit{F. Bigolin} and \textit{F. Serra Cassano}, Adv. Calc. Var. 3, No. 1, 69--97 (2010; Zbl 1188.53027) Full Text: DOI References: [1] Ambrosio L., J. Geom. Anal. 16 pp 2– (2006) [2] Arena G., Calc. Var. PDEs 35 pp 4– (2009) [3] DOI: 10.1007/s00526-006-0076-3 · Zbl 1206.35240 · doi:10.1007/s00526-006-0076-3 [4] Citti G., Commun. Contemp. Math. 8 pp 5– (2006) [5] Danielli D., Amer. J. Math. 130 pp 2– (2008) [6] Danielli D., J. Differential Geom. 81 pp 2– (2009) [7] Franchi B., Math. Ann. 321 pp 479– (2001) · Zbl 1057.49032 · doi:10.1007/s002080100228 [8] Franchi B., Comm. Analysis and Geometry 11 pp 909– (2003) [9] Franchi B., Journal Geometric Analysis 13 pp 421– (2003) [10] Franchi B., Advances in Math. 211 pp 157– (2007) [11] Kirchheim B., Ann. Scuola Norm. Sup. Pisa Cl. Sci. pp 871– (5) [12] Kruzkov S. N., Math. USSR Sb. 10 pp 217– (1970) · Zbl 0215.16203 · doi:10.1070/SM1970v010n02ABEH002156 [13] Magnani V., J. Reine Angew. Math. 619 pp 203– (2008) [14] Pauls S. D., Indiana Univ. Math. J. 53 pp 49– (2004) · Zbl 1076.49025 · doi:10.1512/iumj.2004.53.2293 [15] Pauls S. D., Comm. Math. Helv. 81 pp 337– (2006) · Zbl 1153.53305 · doi:10.4171/CMH/55 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.