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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615005665&_mathId=si1.gif&_user=111111111&_pii=S0022039615005665&_rdoc=1&_issn=00220396&md5=2b8f7669ba408f0700a0d3685d9a530a" title="Click to view the MathML source">Sⁿclass="mathContainer hidden">class="mathCode">${\mathbb{S}}^n$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615005665&_mathId=si2.gif&_user=111111111&_pii=S0022039615005665&_rdoc=1&_issn=00220396&md5=bae47144cc638fb086e0e2f06caba4e3" title="Click to view the MathML source">n≥5class="mathContainer hidden">class="mathCode">$n\ge 5$, 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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615005665&_mathId=si3.gif&_user=111111111&_pii=S0022039615005665&_rdoc=1&_issn=00220396&md5=5ef00a4a944bc8c85c6e22be3ca2e0ca" title="Click to view the MathML source">SO(4)class="mathContainer hidden">class="mathCode">$\mathrm{SO}(4)$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615005665&_mathId=si4.gif&_user=111111111&_pii=S0022039615005665&_rdoc=1&_issn=00220396&md5=c78f2fe707c35cb32f0d7046f0995f9d" title="Click to view the MathML source">SO(5)class="mathContainer hidden">class="mathCode">$\mathrm{SO}(5)$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615005665&_mathId=si5.gif&_user=111111111&_pii=S0022039615005665&_rdoc=1&_issn=00220396&md5=73966a25e9dfe80bbdbe4a2616b12dc5" title="Click to view the MathML source">SO(6)class="mathContainer hidden">class="mathCode">$\mathrm{SO}(6)$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615005665&_mathId=si57.gif&_user=111111111&_pii=S0022039615005665&_rdoc=1&_issn=00220396&md5=5e271f74ad5740a6d69e555c196441c8" title="Click to view the MathML source">SO(7)class="mathContainer hidden">class="mathCode">$\mathrm{SO}(7)$ there exist two infinite families of harmonic self-maps.