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DOI: 10.23952/cot.2027.18
Received October 20, 2025; Accepted April 18, 2026; Published online October 26, 2026
Abstract. The Weierstrass–Enneper representation establishes a fundamental connection between harmonic mappings and isothermal parametrizations of minimal surfaces. In this article, we employ the harmonic shear technique to construct harmonic mappings that arise as projections of minimal surfaces. Specifically, we obtain novel minimal surfaces defined over the shears of convex domains, including the right half-branch of a hyperbola, the right half of the Lemniscate of Bernoulli, and the interior of a parabolic region. Furthermore, we investigate the corresponding conjugate and associated minimal surfaces derived from these constructions. Graphical illustrations are provided to support and visualize the theoretical results. These findings contribute to the growing interplay between geometric function theory and minimal surface theory.
How to Cite this Article:
M. Mohanty, B.K. Chinhara, Construction of minimal surfaces lying over shears of some convex domains, Commun. Optim. Theory 2027 (2027) 18.