Harold William Rosenberg (born 19 February 1941 in New York City) is an American mathematician who works on differential geometry.
[2] In 1993, he studied the hypersurfaces in Euclidean space with a given constant value of an elementary symmetric polynomial of the shape operator, known as a higher-order mean curvature.
As an application, he was able to derive some rigidity results for complete surfaces with constant higher-order mean curvature.
In 2004, he and Uwe Abresch extended the classical Hopf differential, discovered by Heinz Hopf in the 1950s, from the setting of surfaces in three-dimensional Euclidean space to the setting of surfaces in products of two-dimensional space forms with the real line.
As an application, they were able to show that any immersed sphere of constant mean curvature must be rotationally symmetric, thereby extending a classical theorem of Alexandrov.