科研之友
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摘要
We settle a question posed by Umehara and Yamada, which generalizes a completeness lemma useful in differential geometry. %26lt;br%26gt;The following answers affirmatively a question posed by Umehara and Yamada [7, Question C]. %26lt;br%26gt;THEOREM. Let f be a holomorphic function on {vertical bar zeta vertical bar %26gt; 1} subset of C such that f f({vertical bar zeta vertical bar %26gt; 1}) subset of C\{0} and let n be a non-negative integer. If every real-analytic curve gamma : [0, 1) -%26gt; {vertical bar zeta vertical bar %26gt; 1} tending to infinity satisfies %26lt;br%26gt;(1) integral(gamma)vertical bar log zeta vertical bar(n vertical bar)f(zeta)(vertical bar) vertical bar d zeta vertical bar = infinity, %26lt;br%26gt;then f is meromorphic at infinity.
- 出版日期2014-6
