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math.DG2021★ 1 cited
Vector fields with big and small volume on the 2-sphere
Rui Albuquerque
We consider the problem of minimal volume vector fields on a given Riemann surface, specialising on the case of , that is, the arbitrary radius 2-sphere with two antipodal…
math.DG2021
New Hsiung-Minkowski identities
R. Albuquerque
We find the first three most general Minkowski or Hsiung-Minkowski identities relating the total mean curvatures , of degrees , of a closed hypersurface immersed…
math.DG2021
The Euler characteristic of hypersurfaces in space forms and applications to isoparametric hypersurfaces
R. Albuquerque
We revisit Allendoerfer-Weil's formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, first taking some time to re-prove it while…