On Invariants of Constant 𝑝-Mean Curvature Surfaces in the Heisenberg Group 𝐻₁

Abstract

One primary objective in submanifold geometry is to discover fascinating and significant classical examples of 𝐻₁. 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.