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<p>From the well-known Weierstrass–Enneper representation, it is clear that a univalent harmonic mapping admits a minimal surface lift if and only if its dilatation is square of an analytic function. Motivated by this characterization, this article explores convex and close-to-convex harmonic mappings under the constraint that their dilatations are squares of analytic functions. We derive coefficient bounds, growth estimates, Baernstein-type integral mean inequalities, and surface area estimates for the minimal surfaces associated with these classes and establish the sharpness of several results.</p>

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On Minimal Surfaces Through the Lens of Univalent Harmonic Mappings

  • 期刊论文

  • 发表日期：

    2026年5月23日

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  • Jasbir Parashar,
  • Anbareeswaran Sairam Kaliraj

摘要

From the well-known Weierstrass–Enneper representation, it is clear that a univalent harmonic mapping admits a minimal surface lift if and only if its dilatation is square of an analytic function. Motivated by this characterization, this article explores convex and close-to-convex harmonic mappings under the constraint that their dilatations are squares of analytic functions. We derive coefficient bounds, growth estimates, Baernstein-type integral mean inequalities, and surface area estimates for the minimal surfaces associated with these classes and establish the sharpness of several results.