Robert Finn (born February 10, 1922, Los Angeles, California; died September 24, 2022, Stanford, California) was an American mathematician renowned for his contributions to differential geometry, particularly his work on capillary surfaces and minimal surfaces. He spent the majority of his career as a professor at Stanford University.
Finn obtained his Ph.D. from Syracuse University in 1950 under the supervision of Paul Berg.
His research focused primarily on the mathematical theory of capillarity, a field he essentially pioneered. He developed deep insights into the behavior of liquid interfaces, especially in the presence of gravity and contact angles. His work provided a rigorous mathematical framework for understanding phenomena such as the shape of droplets and menisci.
Finn is particularly known for his "Finn's Theorem" regarding the existence and uniqueness of solutions to the capillary equation. This theorem established fundamental limits on the size of containers that can hold a liquid without spilling.
Beyond capillarity, Finn also made significant contributions to the theory of minimal surfaces.
Finn was a member of the National Academy of Sciences. He received numerous awards and honors throughout his career, recognizing his profound impact on mathematics and related fields. He was known for his rigorous approach and his ability to connect abstract mathematical concepts to concrete physical phenomena.