Polyharmonic hypersurfaces into complex space forms

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-04-20 DOI:10.1007/s10231-024-01452-0

José Miguel Balado-Alves

引用次数: 0

Abstract

We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for \(\mathbb{C}\mathbb{P}^n\) and \(\mathbb{C}\mathbb{H}^n\), respectively. Moreover, we study the stability of biharmonic hypersurfaces and compute the normal index for a large family of solutions.

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将多谐超曲面转化为复杂空间形式

我们描述了作为高阶能量函数临界点出现的复数空间形式的同质超曲面的特征。因此，我们分别得到了 \(\mathbb{C}\mathbb{P}^n\) 和 \(\mathbb{C}\mathbb{H}^n\) 的存在和不存在结果。此外，我们还研究了双谐波超曲面的稳定性，并计算了一大系列解的正常指数。

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.