Corrections to: "The Willmore flow of Hopf-tori in the 3-sphere"

TL;DR

This erratum corrects logical mistakes in a previous paper on the Willmore flow of Hopf-tori in the 3-sphere, providing counterexamples and refined assertions to ensure mathematical accuracy.

Contribution

The paper identifies and corrects specific errors in the original work, including counterexamples and refined statements to improve the validity of the results.

Findings

Correction of two wrong assertions in Theorem 1

Counterexample demonstrating the optimality of the corrected statement

Clarification of the formulation of Proposition 6

Abstract

This erratum addresses a logical mistake in the author's article [Jakob, R. The Willmore flow of Hopf-tori in the $3$-sphere. Journal of Evolution Equations 23, No. 72 (2023)] which resulted in two wrong assertions in parts (II) and (III) of Theorem 1 in the author's cited paper and in an inaccuracy in the formulation of the second part of Proposition 6 in that paper. We will not only point out these mistakes and their corrections, but we will additionally give a concrete counterexample to Statement (III) in Theorem 1 of the author's cited article which will automatically imply the optimality of the corrected version of that statement, as it is formulated in this erratum.