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
SN - 0003-9527
VL - 141
SP - 105
EP - 116
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -