Infinite families of harmonic self-maps of spheres

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• 作者：Anna Siffert¹ ; ^{siffert@mpim-bonn.mpg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：58E20 ; 34B15 ; 55M25
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 February 2016
• 年：2016
• 卷：260
• 期：3
• 页码：2898-2925
• 全文大小：456 K

文摘

For each of the spheres Sⁿ${\mathbb{S}}^n$, n≥5$n\ge 5$, we construct a new infinite family of harmonic self-maps, and prove that their members have Brouwer degree ±1 or ±3. These self-maps are obtained by solving a singular boundary value problem. As an application we show that for each of the special orthogonal groups SO(4)$\mathrm{SO}(4)$, SO(5)$\mathrm{SO}(5)$, SO(6)$\mathrm{SO}(6)$ and SO(7)$\mathrm{SO}(7)$ there exist two infinite families of harmonic self-maps.