# Lipman Bers

Lipman Bers (May 22, 1914 – October 29, 1993) was a Latvian-born American mathematician, known for his research on pseudoanalytic functions, Riemann surfaces, and Kleinian groups. He was an invited speaker at the International Congress of Mathematicians in 1958 in Edinburgh. He was the president of the American Mathematical Society from 1975 to 1976.

## Quotes

• Minimal surfaces are of interest in various branches of mathematics. In the calculus of variations they appear as surfaces of least area, in differential geometry as surfaces of vanishing mean curvature. In gas dynamics the equation of minimal surfaces,
(1)          ${\displaystyle (1+\phi _{x}^{2})\phi _{yy}-2\phi _{x}\phi _{y}\phi _{xy}+(1+\phi _{y}^{2})\phi _{xx}=0}$,
is interpreted as the potential equation of a hypothetical gas, which yields flows closely approximating adiabatic flows of low Mach number. This interpretation, due to Chaplygin,... has been used extensively in recent aerodynamical literature. In the general theory of partial differential equations, finally, equation (1) appears as the the simplest nonlinear equation of elliptic type. From the point of view of this theory it is natural to restrict ourselves to minimal surfaces in three-space admitting a non-parametric representation.
• "Singularities of minimal surfaces." In Proc. Intern. Math. Congress, Cambridge, Mass. , vol. 2, pp. 157–164. 1950. (quote from p. 157)
• The theory of analytic functions of a complex variable occupies a central place in analysis and it is not surprising that mathematical literature abounds in generalizations. In some generalizations one extends the domain of the functions considered, or their range, or both (functions of several complex variables, analytic functions with values in a vector space or an algebra, analytic functions of hyper-complex variables, analytic operators, etc.) If we restrict ourselves to functions from plane domains to plane domains, or, more generally, from Riemann surfaces to Riemann surfaces, we encounter two well known and very useful generalizations of analytic functions: interior functions and quasi-conformal functions. Interior functions ... have all topological properties of analytic functions and no others. As a matter of fact, they may be defined as functions which can be made analytic by a homeomorphism of the domain of definition. Quasi-conformal functions ... are interior functions subject to an additional metric condition. If the functions are assumed to be continuously differentiable mappings, this additional condition requires that infinitesimal circles be taken into infinitesimal ellipses of uniformly bounded eccentricity.

## Quotes about Lipman Bers

• Bers' paper [15], in which he shows that a C-linear algebra isomorphism between the rings of holomorphic functions on two surfaces is induced by a conformal map between them, appeared in 1948 and started a whole industry. ...
[15] L. Bers, On the ring of analytic functions, Bull. Amer. Math. Soc. 54 (1948), 311-315.