On the Boundary Behavior of Minimal Surfaces.
On the Boundary Behavior of Minimal Surfaces.
复制标题
DOI：
10.1073/pnas.37.2.103
复制
发表时间：
1951-02
影响因子：
11.1
通讯作者：
Hans Lewy
中科院分区：
文献类型：
--
作者：
Hans Lewy
7我们将明确地表述这类结果：设S是在0上对称的点集，位于两个封闭的圆形区域R1：iz a rand R2：iz + al <r，其中我们有ac 2r。然后所有的零的所有（奇）极值多项式在S以外的一个简单的零在0，谎言在封闭的区域R，一个IR 2。4.同样，结果零点的衍生物有效的条件下对称的高阶7相对于原点可以扩展到极值多项式下相应的对称性假设。* 高等研究院，普林斯顿，新泽西。1 Jahresbericht d. Deutschen Math.Vereinigung，31，125 - 138（1922）.
be treated and result about the distribution of roots obtained, analogous to facts concerning zeros of derivatives of polynomials possessing such symmetry properties.7 We shall explicitly formulate but one result of this kind: Let S be a pointset symmetric in 0 and lie in the two closed circular regions R,: iz a rand R2: iz + al < r where we have ac 2r. Then all zeros of all (odd) extremal polynomials on S other than a simple zero at 0, lie in the closed regions R, an I R2. 4. Similarly, results on zeros of derivatives valid under conditions of symmetry of higher order7 with respect to the origin can be extended to extremal polynomials under corresponding symmetry assumptions. * The Institute for Advanced Study, Princeton, New Jersey. 1 Jahresbericht d. Deutschen Math. Vereinigung, 31, 125-138 (1922).