Abstract
A metric ds2 admits a Σ-realization if there is a realization of it in E3 in the form of a surface whose boundary lies on a given surface Σ. This paper proves the existence of Σ-realizations of a certain class of metrics of positive curvature for surfaces of quite general form, and describes a number of possible Σ-realizations of the given metric. The proof is based on a consideration of a nonlinear boundary-value problem for immersion equations. Bibliography: 3 titles.
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