Axisymmetric solutions of the λ-singular minimal surface equation

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KAYA S., López R.

Acta Mathematica Hungarica, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s10474-026-01613-y
  • Dergi Adı: Acta Mathematica Hungarica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
  • Anahtar Kelimeler: Phase plane, Rotational surface, Singular minimal surface, Weighted mean curvature
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Ankara Üniversitesi Adresli: Evet

Özet

Given a unit vector v→∈R3 and λ,α∈R, a surface Σ⊂R3 is called λ-singular minimal surface if its mean curvature H satisfies H(p)=α⟨N(p),v→⟩⟨p,v→⟩+λ for all p∈Σ, where N is the unit normal to Σ. In this paper, we study the axisymmetric solutions of this equation, identifying two types of surfaces depending on whether the rotation axis is parallel or orthogonal to v→. For the first type, we prove the existence of surfaces that orthogonally intersect the rotation axis. For the second type, we provide a complete geometric description.