Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The article is 'Hadamard and Calabi Yau conjectures on negatively curved an minimal surfaces' Nadirashvili. In the proof of proposition 4.3 it asserts that the function y is holomorphic. I'm not sure about it (actually i think it is false). What do you think about it? Thank you for your help.

share|cite|improve this question

1 Answer 1

up vote 1 down vote accepted

I agree, this part is wrong as stated, although the ideas behind it are sound. Pascal Collin and Harold Rosenberg did a great service to the community by publishing the note

P. Collin and H. Rosenberg, Notes sur la démonstration de N. Nadirashvili des conjectures de Hadamard et Calabi-Yau, Bull. Sci. Math. 123 (1999), no. 7, 563–575.

in which they clarify and correct various details. In particular, the appendix of this note contains a cleaned-up proof of Proposition 3.4, which provides the missing details concerning the zeroes of the various functions involved.

References: Collin-Rosenberg, Nadirashvili (also preprint), and first part of this discussion.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.