Details

Autor(en) / Beteiligte

• Fernández, Isabel
• Mira, Pablo

Titel

Elliptic Weingarten surfaces: Singularities, rotational examples and the halfspace theorem

Ist Teil von

• Nonlinear analysis, 2023-07, Vol.232, p.113244, Article 113244

Ort / Verlag

Elsevier Ltd

Erscheinungsjahr

2023

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We show by phase space analysis that there are exactly 17 possible qualitative behaviors for a rotational surface in R3 that satisfies an arbitrary elliptic Weingarten equation W(κ1,κ2)=0, and study the singularities of such examples. As global applications of this classification, we prove a sharp halfspace theorem for general elliptic Weingarten equations of finite order, and a classification of peaked elliptic Weingarten ovaloids with at most 2 singularities. In the case that W is not elliptic, we give a negative answer to a question by Yau regarding the uniqueness of rotational ellipsoids.