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.