Special Weingarten surfaces with planar convex boundary

Barbara Nelli; Giuseppe Pipoli; Marcos Paulo Tassi

Special Weingarten surfaces with planar convex boundary

Differential Geometry 2024-11-05 v2

Authors: Barbara Nelli , Giuseppe Pipoli , Marcos Paulo Tassi

Abstract

We prove a Ros-Rosenberg theorem in the setting of Special Weingarten surfaces. We show that a compact, connected, embedded, Special Weingarten surface in $\mathhb{R}^3$ with planar convex boundary is a topological disk under mild suitable assumptions.

Keywords

surfaces and embeddings algebraic surfaces surface theory

Cite

@article{arxiv.2406.16511,
  title  = {Special Weingarten surfaces with planar convex boundary},
  author = {Barbara Nelli and Giuseppe Pipoli and Marcos Paulo Tassi},
  journal= {arXiv preprint arXiv:2406.16511},
  year   = {2024}
}

Comments

22 pages, 13 figures. We did slight improvements in the proof of Lemma 4.1, added new figures and corrected some typos

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