0000000000394137

AUTHOR

S. Segura Gomis

Dido's problem in the plane for domains with fixed diameter

We find the connected compact domains in the closed half-plane, with fixed area and diameter, which minimize the relative perimeter.

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A Dido problem for domains in ?2 with a given inradius

We find which are the simply connected domains in ℝ2 satisfying the Dido condition for a straight shoreline, with a given area A and a fixed inradius ϱ, which minimize the length of the free boundary. There are three different cases according to the values of A and ϱ.

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