The following theorem is commonly attributed to Jacques Hadamard.

Assume $\Sigma$ is a smooth locally convex immersed surface in the Euclidean space. Then $\Sigma$ is embedded and bounds a convex set.

Many authors refer to Hadamard's *Sur certaines propriétés des trajectoires en Dynamique* (1897)
(for example, James Stoker in his *Über die Gestalt der positiv...* (1936)).

Likely the statement is there, but the paper is long, it is in French and often the statements are not clearly marked; I was searching for it for several days. I asked a friend and she said that it was there 20 years ago, but she could not find it; she also said that it was not easy to extract it from what is written ( = one has to think). [For sure the word *immersion* is not there.]

I hope someone here knows this paper and can help me.

**P.S.** Now I see it this way: Stoker was the first who had formulated and proved the theorem; at the beginning of his paper he attributed the theorem to Hadamard because it almost follow from item 23 in his paper. After Stoker everyone did the same.