32 citations · 142 across the 27 of their papers we have counts for
7 papers · 1 filter
General rigidity principles for stable and minimal elastic curves
Tatsuya Miura, Kensuke Yoshizawa
For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers…
Pinned planar p-elasticae
Tatsuya Miura, Kensuke Yoshizawa
Building on our previous work, we classify all planar -elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. A…
Li-Yau type inequality for curves in any codimension
Tatsuya Miura
For immersed curves in Euclidean space of any codimension we establish a Li--Yau type inequality that gives a lower bound of the (normalized) bending energy in terms of multiplicit…
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'…
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.…
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…
On the isoperimetric inequality and surface diffusion flow for multiply winding curves
Tatsuya Miura, Shinya Okabe
In this paper we establish a general form of the isoperimetric inequality for immersed closed curves (possibly non-convex) in the plane under rotational symmetry. As an application…