论文标题
liouville型定理在圆形或领域以外的限制有限秩序的功能
Liouville-type theorems with constraints outside of small sets on circles or spheres for functions of finite order
论文作者
论文摘要
我们证明，有限顺序在有限尺寸的真实空间上的次谐波函数从某些渐近小的套件外部边界，在球体上的某些小集合在各个地方都界定。因此，有限顺序，有限顺序的全部和多余的函数以及有限顺序的全部和多余的函数，以及从上面的上方界限的有限顺序的凸面或谐波函数是恒定的。我们的结果和证明方法对于一个复杂变量的功能也是新的。
We prove that subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some asymptotically small sets on spheres, are bounded from above everywhere. It follows that subharmonic functions of finite order on the complex plane, entire and plurisubharmonic functions of finite order, and convex or harmonic functions of finite order bounded from above outside of such sets on spheres are constant. Our results and methods of proof are also new for functions of one complex variable.
