### Biography

Manfredo Perdigão do Carmo, Brazilian geometer (Maceió 15 August 1928 – Rio de Janeiro 30 April 2018)

Published more than 60 scientific papers in top-quality reviews (2 of them in Annals of Mathematics)

Published Differential geometry of curves and surfaces in English (1976), translated into Spanish, German and Chinese languages and used worldwide.

### ACHIEVEMENTS

Introduced the concept of weak stability with Barbosa and Eschenburg (1988)

Obtained a condition in order to Mn compact variety from Euclidean space Rn+p be included in Rn+1 published in Archiv der Mathematik with wide recognition

With M.F. Elbert proposed the notion of finite total curvature for a complete hypersurface of the euclidean space with vanishing scalar curvature

Proposed that given a complete surface with non-null constant mean curvature its Gaussian image contains a maximal circle of sphere (1981)

With N. Wallach described the moduli space as a convex set with stratified boundary (1969-71)

With F. Warner proved that a compact surface in S^{3} whose extrinsic curvature is non-negative is an embedded sphere (1970)

With J.L. Barbosa proved that an orientable minimal surface in R^{3} whose Gaussian image has area less than 2 π is stable (1976)

With Peng proved that a complete, orientable and stable minimal surface in R^{3} is a plane or Do Carmo-Peng-Schoen theorem (1979)

With M. Dajczer & F. Mercuri classified conformally flat hypersurfaces in space forms of dimension greater than or equal to five known as conformal surgery (1985)

With H. Alencar & A.G. Colares proved that a constant scalar curvature compact hypersurface of a space form is a geodesic sphere (1993)

With H. Alencar & W. Santos proved a gap theorem for compact hypersurfaces of scalar curvature one in spheres (2002)

### HONORS

Invited Lecturer to International Congress of Mathematicians, Finland, 1978

TWAS Prize in Mathematics (1992)

### EPONYMY

Alencar-do Carmo theorem

do Carmo surface

Barbosa-do Carmo theorem

Chern-do Carmo-Kobayashi conjecture (1970)

Chern-do Carmo-Kobayashi rigidity theorem (1970)

Do Carmo-Dajczer surfaces

do Carmo-Wallach classification

do Carmo-Wallach theorem

do Carmo-Zhou theorem (1999)

do Carmo-Peng theorem (1979)

do Carmo-Warner theorem

Do Carmo-Fernandez theorem