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Preprint in the OpenAI Math release

Smooth isometric immersions of closed surfaces into Euclidean four-space

OpenAI

Abstract

Every closed smooth Riemannian surface admits a smooth isometric immersion into Euclidean four-space, without an orientability assumption. This resolves the closed-surface form of the classical four-dimensional isometric-immersion problem.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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