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Symmetry, Integrability and Geometry: Methods and Applications, 2025, Volume 21, 011, 25 pp.
DOI: https://doi.org/10.3842/SIGMA.2025.011 (Mi sigma2128) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Invariants of Constant $p$-Mean Curvature Surfaces in the Heisenberg Group $H_1$

Hung-Lin Chiuab, Sin-Hua Laic, Hsiao-Fan Liude

a Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
b National Center for Theoretical Sciences, Taipei, Taiwan
c Fundamental Education Center, National Chin-Yi University of Technology, Taichung, Taiwan
d Department of Applied Mathematics, National Chung Hsing University, Taiwan
e Department of Applied Mathematics, National Chung Hsing University, Taiwan
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DOI: https://doi.org/10.3842/SIGMA.2025.011
URL: https://www.emis.de/journals/SIGMA/2025/011/
Abstract: One primary objective in submanifold geometry is to discover fascinating and significant classical examples of $H_1$. In this paper which relies on the theory we established in [Adv. Math. 405 (2022), 08514, 50 pages, arXiv:2101.11780] and utilizing the approach we provided for constructing constant $p$-mean curvature surfaces, we have identified intriguing examples of such surfaces. Notably, we present a complete description of rotationally invariant surfaces of constant $p$-mean curvature and shed light on the geometric interpretation of the energy $E$ with a lower bound.
Keywords: Heisenberg group, Pansu sphere, $p$-minimal surface, Codazzi-like equation, rotationally invariant surface.
Funding agency Grant number
National Center for Theoretical Sciences 112-2115-M-007-009-MY3
110-2115-M-167-002-MY2
112-2115-M-167-002-MY2
112-2628-M-032-001-MY4
The first author’s research was supported in part by NSTC 112-2115-M-007-009-MY3. The second author’s research was supported in part by NSTC 110-2115-M-167-002-MY2 and NSTC 112-2115-M-167-002-MY2. The third author’s research was supported in part by NSTC 112 2628-M-032-001-MY4.
Received: April 15, 2024; in final form February 4, 2025; Published online February 18, 2025
Bibliographic databases:
Document Type: Article
MSC: 53A10, 53C42, 53C22, 34A26
Language: English
Citation: Hung-Lin Chiu, Sin-Hua Lai, Hsiao-Fan Liu, “On Invariants of Constant $p$-Mean Curvature Surfaces in the Heisenberg Group $H_1$”, SIGMA, 21 (2025), 011, 25 pp.
Citation in format AMSBIB
\Bibitem{ChiLaiLiu25}
\by Hung-Lin~Chiu, Sin-Hua~Lai, Hsiao-Fan~Liu
\paper On Invariants of Constant $p$-Mean Curvature Surfaces in the Heisenberg Group $H_1$
\jour SIGMA
\yr 2025
\vol 21
\papernumber 011
\totalpages 25
\mathnet{http://mi.mathnet.ru/sigma2128}
\crossref{https://doi.org/10.3842/SIGMA.2025.011}
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