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The shape of a liquid surface bounded by an acute or obtuse planar angularsector is considered by using classical analysis methods. For acute angularsectors the two principal curvatures are of the order of the (fixed) meancurvature. But for obtuse sectors, the principal curvatures both diverge as thevertex is approached. The power-law divergence becomes stronger with increasingopening angle. Possible implications of this contrasting behavior aresuggested.Comment: 19 pages, 9 figures, LaTeX; submitted to The European Physics Journal  E; v2: Introduction was revised (a number of references added), minor changes  to the main part (mostly typos), former Implications subsection was almost  entirely rewritten and is now called Experimental Realizations (experimental  results and two figures added); v3: Introduction was slightly modified, four  references added; v4: Title was modified, section Calculation was  significantly modified (subsections Bounary Problem and Horizontal Solution  almost entirely rewritten, minor changes to the other subsections),  subsection Curvature in section Discussion was revised, one reference adde

Characteristic angles in the wetting of an angular region: Surface shape