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Manfredo Perdigão do Carmo

Manfredo Perdigão do Carmo, Brazilian geometer (Maceió 15 August 1928 -


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 to 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 S3 whose extrinsic curvature is non-negative is an embedded sphere (1970)


With J.L. Barbosa proved that an orientable minimal surface in R3 whose Gaussian image has area less than 2 π is stable (1976)


With Peng proved that a complete, orientable and stable minimal surface in R3 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