Regularity of C1 smooth surfaces with prescribed p-mean curvature in the Heisenberg group
By Jih-Hsin Cheng, Jenn-Fang Hwang, Paul Yang. 2007
58 citations recorded by the source corpus.
We consider a C1 smooth surface with prescribed p (or H)-mean curvature in the 3-dimensional Heisenberg group. Assuming only the prescribed p-mean curvature $${H\in C^{0},}$$ we show that any characteristic curve is C2 smooth and its (line) curvature equals − H in the nonsingular domain. By introducing characteristic coordinates and invoking the jump formulas along characteristic curves, we can prove that the Legendrian (or horizontal) normal gains one more derivative. Therefore the seed curves are C2 smooth. We also obtain the uniqueness of characteristic and seed curves passing through a common point under some mild conditions, respectively. These results can be applied to more general situations.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/4bb5caa628f14d4766c9194a7b1cdf36fc02f7b2
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In Applied Mathematics
- Giovanna Citti
- Maria Manfredini
- Luca Capogna
- Manuel Ritor'e
- Jun-cheng Wei
- Francesco Serra Cassano
- Manuel del Pino
- M. Kowalczyk
Citations in the corpus
- Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1 (2010, methodology): “In this sense our results are more specialized and less general than the ones in [9].”
- Examples of area-minimizing surfaces in the subriemannian Heisenberg group H^1 with low regularity (2008, background): “These cones are a generalization of the one obtained by Cheng, Hwang and Yang [9, Ex.”