Carathéodory conjecture
From Wikipedia, the free encyclopedia
In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a session of the Berlin Mathematical Society in 1924.[1] Carathéodory did publish a paper on a related subject,[2] but never committed the conjecture into writing. In,[3] John Edensor Littlewood mentions the conjecture and Hamburger's contribution[4] as an example of a mathematical claim that is easy to state but difficult to prove. Dirk Struik describes in [5] the formal analogy of the conjecture with the Four Vertex Theorem for plane curves. Modern references to the conjecture are the problem list of Shing-Tung Yau,[6] the books of Marcel Berger,[7][8] as well as the books.[9][10][11][12]
The conjecture has had a troubled history with published proofs in the analytic case [13][14] which contained gaps,[15] and claims of proof in the general smooth case[16] which have not been accepted for publication.