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math.DG2026
Minimal total absolute curvature for equiaffine immersions
Yuta Yamauchi
Koike (2001) defined the Lipschitz--Killing curvature and established a Chern--Lashof type inequality for equiaffine immersions of arbitrary codimensions. In this paper, we study t…
math.DG2024
The total absolute curvature of submanifolds with singularities
Yuta Yamauchi
In this paper, we give a generalization of the Chern-Lashof theorem for submanifolds with singularities called frontals in Euclidean space. We prove that, for an -dimensional ad…
math.DG2024★ 1 cited
The total absolute curvature of closed curves with singularities
Atsufumi Honda, Chisa Tanaka, Yuta Yamauchi
In this paper, we give a generalization of Fenchel's theorem for closed curves as frontals in Euclidean space . We prove that, for a non-co-orientable closed frontal…