Jianguo Cao
Jianguo Cao, who passed on in June, was a good mathematician and correspondent. It was his paper with Itai Benjamini on the isoperimetric problem in surfaces of revolution that first proved, for example, that isoperimetric curves in the paraboloid {z=x2+y2} are horizontal circles. Many papers followed by many mathematicians, including me.
After writing a joint paper with Hugh Howards and Michael Hutchings and returning from leave, in cleaning out old files I discovered a preprint of Cao’s paper with Benjamini which Cao gave me at the Lehigh Geometry/Topology Conference in June, 1994. I forgot all about it and got interested in the problem two years later. The basic idea of our Theorem 2.1 came from Hutchings in an email message of December 19, 1996. But now I know that the first inspiration came from Cao.
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Shun-Xiang Ouyang:
Dear Prof. Morgan,
I am trying to learn something about isoperimetric problem. Thank you very much for your writing. I am sorry to hear that Prof. Cao has passed.
It seems that the name of Prof. Cao is not correctly spelled in your note and in the paper you mentioned.
That is, “Jinguo” should be “Jianguo”.
In your paper you cite:
“Itai Benjamini and Jinguo Cao, A new isoperimetric theorem for surfaces of variable curvature”.
It seems that some words above should be
“Jianguo” “isoperimetric comparison theorem”.
Best regards,
Yours sincerely,
2 September 2011, 11:45 amOuyang.
Frank Morgan:
Dear Ouyang, Thanks very much for your interest and for pointing out that recurrent typo, which I have fixed in the post. —fm
2 September 2011, 6:08 pm