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Seminário de Análise - 27/06/2025 às 10:30

O seminário ocorrerá no próximo dia 27/06, às 10h30, no auditório do MAT

 

Título:  On the space of Cregular curves on sphere with constrained curvature

Palestrante: Cong Zhou (UFF)

Abstract: We prove that the C0 and Ctopologies are the same on the set of C1
regular curves in the 2-sphere whose tangent vectors are Lipschitz continuous, and the
a.e. existing geodesic curvatures are essentially bounded in an open interval.

    Besides, we study the subset consisting of curves that start and end at given points
with given directions, and prove that this subset is a Banach manifold.

    Furthermore, we study Cregular curves in the 2-sphere that start and end at given
points with given directions, whose tangent vectors are Lipschitz continuous, and their
a.e. existing geodesic curvatures have essentially bounds in an open interval. Especially,
we show that a Cregular curve is such a curve if and only if the infimum of its lower
curvature and the supremum of its upper curvature are constrained in the same interval.

References:
[1] C. Zhou On the space of Cregular curves on sphere with constrained curvature. Results in Mathematics, v. 76, p. 223, 2021.
[2] C. Zhou The geometry of Cregular curves in sphere with constrained curvature. J. Geom. Anal. 31 (2020), no. 6, 5974–5987.


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