Abstract
A theorem of Hartman–Wintner enables us to find a nonzero homogeneous polynomial approximate to the difference of two solutions of an elliptic partial differential equation of second order. This theorem plays a crucial role in the study of an umbilical point on each of a special Weingarten surface, a surface with constant anisotropic mean curvature and a Willmore surface. In the present paper, we will survey the roles of Hartman–Wintner’s theorem on these surfaces.
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