Elliptic Weingarten surfaces of minimal type invariant by left translations in \(\textrm{Sol}_3\)

IF 0.9 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-12 DOI:10.1007/s10231-026-01674-4

Albetã C. Mafra, Carlos Peñafiel, Erick J. Palacios Escobar

引用次数: 0

Abstract

In this article, we show the existence and uniqueness of a family of complete elliptic Weingarten surfaces of minimal type, which are invariant by a uniparametric group of horizontal translation. Moreover, we give a complete description of the generating curve of each of these surfaces when the elliptic function satisfies \(f(x)>0\) for \(x\ne 0\).

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中的最小型不变椭圆Weingarten曲面的左平移 \(\textrm{Sol}_3\)

本文通过水平平移的单参数群证明了一类极小型完全椭圆Weingarten曲面的存在唯一性。此外，对于\(x\ne 0\)，我们给出了当椭圆函数满足\(f(x)>0\)时，每个曲面的生成曲线的完整描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.