Growth of proper holomorphic maps and tropical power series

详细信息    查看全文

• 作者：Evgeny Abakumov^a ; ^{evgueni.abakoumov@u-pem.fr" class="auth_mail" title="E-mail the corresponding author} ; Evgueni Doubtsov^b ; ^c ; ^{dubtsov@pdmi.ras.ru" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Comptes Rendus Mathematique
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：354
• 期：5
• 页码：465-469
• 全文大小：263 K

文摘

Motivated by a question of J. Globevnik, we show that a proper holomorphic immersion of the unit disk class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16300024&_mathId=si1.gif&_user=111111111&_pii=S1631073X16300024&_rdoc=1&_issn=1631073X&md5=e13afa14ba7d5be316df41165354a56d" title="Click to view the MathML source">Dclass="mathContainer hidden">class="mathCode">$\mathbb{D}$ into class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16300024&_mathId=si138.gif&_user=111111111&_pii=S1631073X16300024&_rdoc=1&_issn=1631073X&md5=5adc308de042ec2b944d0f4b9b2dc326" title="Click to view the MathML source">C²class="mathContainer hidden">class="mathCode">${\mathbb{C}}^2$ or a proper holomorphic embedding class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16300024&_mathId=si16.gif&_user=111111111&_pii=S1631073X16300024&_rdoc=1&_issn=1631073X&md5=9b068e72cfe7545ad016b86c560c72ae" title="Click to view the MathML source">f:D→C³class="mathContainer hidden">class="mathCode">$f:\mathbb{D}\to {\mathbb{C}}^3$ may have arbitrary growth. Also, using tropical power series, we characterize those radial weights w   on the complex plane for which there exist class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16300024&_mathId=si36.gif&_user=111111111&_pii=S1631073X16300024&_rdoc=1&_issn=1631073X&md5=f827f3ce44ae64b76ba9c110a2728e9b" title="Click to view the MathML source">n∈Nclass="mathContainer hidden">class="mathCode">$n\in \mathbb{N}$ and a proper holomorphic map class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16300024&_mathId=si5.gif&_user=111111111&_pii=S1631073X16300024&_rdoc=1&_issn=1631073X&md5=484d1158c503a29ccf72ca38da7e9b56" title="Click to view the MathML source">f:C→Cⁿclass="mathContainer hidden">class="mathCode">$f:\mathbb{C}\to {\mathbb{C}}^n$ such that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16300024&_mathId=si6.gif&_user=111111111&_pii=S1631073X16300024&_rdoc=1&_issn=1631073X&md5=7b67400111f08120349fd0589f82b94e" title="Click to view the MathML source">|f(z)|class="mathContainer hidden">class="mathCode">$|f(z)|$ is equivalent to class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631073X16300024&_mathId=si7.gif&_user=111111111&_pii=S1631073X16300024&_rdoc=1&_issn=1631073X&md5=687d0e53d3b15bc7dd0ba7f24d61c2ea" title="Click to view the MathML source">w(z)class="mathContainer hidden">class="mathCode">$w(z)$.