Leon Simon, born 6 July 1945, received his BSc from the University of Adelaide in 1967, and his PhD in 1971 from the same institution, under the direction of James H. Michael.

The main tool is an infinite-dimensional extension and corollary of the Łojasiewicz inequality, using the standard Fredholm theory of elliptic operators and Lyapunov-Schmidt reduction.

[11][12] Other authors have made fundamental use of Simon's results, such as Rugang Ye's use for the uniqueness of subsequential limits of Yamabe flow.

Such geometric estimates have proven to be relevant in a number of other important works, such as in Ernst Kuwert and Reiner Schätzle's analysis of Willmore flow and in Hubert Bray's proof of the Riemannian Penrose inequality.

With his thesis advisor James Michael, Simon provided a fundamental Sobolev inequality for submanifolds of Euclidean space, the form of which depends only on dimension and on the length of the mean curvature vector.

[19] Due to the geometric dependence of the Michael−Simon and Hoffman−Spruck inequalities, they have been crucial in a number of contexts, including in Schoen and Shing-Tung Yau's resolution of the positive mass theorem and Gerhard Huisken's analysis of mean curvature flow.

[20][21][22][23] Robert Bartnik and Simon considered the problem of prescribing the boundary and mean curvature of a spacelike hypersurface of Minkowski space.

[24] Using approximation by harmonic polynomials, Robert Hardt and Simon studied the zero set of solutions of general second-order elliptic partial differential equations, obtaining information on Hausdorff measure and rectifiability.

[26] The stable minimal hypersurface theory itself was taken further by Schoen and Simon six years later, using novel methods to provide geometric estimates without dimensional restriction.