Stable periodic projective planes

Ritoré, Manuel

doi:10.1090/S0002-9939-96-03681-7

Stable periodic projective planes
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by Manuel Ritoré

Proc. Amer. Math. Soc. 124 (1996), 3851-3856

DOI: https://doi.org/10.1090/S0002-9939-96-03681-7

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Abstract:

We find all stable projective planes with finite topology which are properly embedded in $\Bbb R^3/\varGamma$, where $\varGamma$ is a discrete subgroup of translations in $\Bbb R^3$. Here stable means second order minimum of the area. The surfaces we obtain are a quotient of the helicoid and quotients of the doubly periodic Scherk surfaces.

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