Instability of rational and polynomial convexity

Abstract

It is shown that rational and polynomial convexity of totally real submanifolds is in general unstable under perturbations that are $C^{\alpha }$-small for any Hölder exponent $\alpha <1$. This complements the result of Løw and Wold that these properties are $C^1$-stable.

V.1 - 4 pages, 1 figure; V.2 - details and comments added, 5 pages, 2 figures; V.3 - minor edits

References in corpus (1)

• Lagrangian isotopy of tori in $S^2\times S^2$ and $\mathbb{C}{P}^2$