Abstract
Since volM ≤ volSn this does not affect the arguments below. The other more serious mistake is that the set Aδ need not be connected so we cannot assume that det (dΦ) has constant sign on this set. This means that the proof of Lemma 6.2 is incomplete as it stands. The author does not see a way of correcting this particular error nor does he know of an alternate proof which is simpler than what is already in the literature. The author would like to mention that Cheeger has written an article [1], which contains a complete and streamlined account on convergence of manifolds with Ricci curvature bounds. Note that this does not affect Theorem 1.1 of [2]. This result is proven in Sects. 3, 4, 5 and does not depend on Sect. 6.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
