On the Boundary Behavior of Minimal Surfaces

Abstract

MA THEMA TICS: H. LEWY be treated and result about the distribution of roots obtained, analogous to facts concerning zeros of derivatives of polynomials possessing such sym- metry properties.7We 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 ex- tremal polynomials under corresponding symmetry assumptions.