TY - JOUR

T1 - Negatively curved sets on surfaces of Constant Mean Curvature in ℝ3 are Large

AU - Huang, Wu Hsiung

AU - Lin, Chun Chi

PY - 1998/3/26

Y1 - 1998/3/26

N2 - It is proved that the negatively curved set M_ on a nonparametric surface M of constant mean curvature in ℝ3 must extend to the boundary ∂M, if M_ is nonempty. For M parametric, if M_ is compactly included in the interior of M , then M_ is at least as large as an extremal domain. The results imply certain convexity results on elliptic partial differential equations. Second-order calculus of variation is employed.

AB - It is proved that the negatively curved set M_ on a nonparametric surface M of constant mean curvature in ℝ3 must extend to the boundary ∂M, if M_ is nonempty. For M parametric, if M_ is compactly included in the interior of M , then M_ is at least as large as an extremal domain. The results imply certain convexity results on elliptic partial differential equations. Second-order calculus of variation is employed.

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U2 - 10.1007/s002050050074

DO - 10.1007/s002050050074

M3 - Article

AN - SCOPUS:0032386814

VL - 141

SP - 105

EP - 116

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -