32 citations · 142 across the 27 of their papers we have counts for
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math.DG2020★ 3 cited
A diameter bound for compact surfaces and the Plateau-Douglas problem
Tatsuya Miura
In this paper we give a geometric argument for bounding the diameter of a connected compact surface (with boundary) of arbitrary codimension in Euclidean space in terms of Topping'…
math.DG2020★ 8 cited
Polar tangential angles and free elasticae
Tatsuya Miura
In this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature.…
math.DG2020★ 3 cited
Geometric inequalities involving mean curvature for closed surfaces
Tatsuya Miura
In this paper we prove some geometric inequalities for closed surfaces in Euclidean three-space. Motivated by Gage's inequality for convex curves, we first verify that for convex s…