32 citations · 142 across the 27 of their papers we have counts for
7 papers · 1 filter
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…
Navier-Stokes equations in a curved thin domain, Part I: uniform estimates for the Stokes operator
Tatsu-Hiko Miura
In the series of this paper and the forthcoming papers [41,42] we study the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Na…
Navier-Stokes equations in a curved thin domain, Part II: global existence of a strong solution
Tatsu-Hiko Miura
We consider the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Navier's slip boundary conditions. When the thickness of the t…
Sharp boundary -regularity of optimal transport maps
Tatsuya Miura, Felix Otto
In this paper we develop a boundary -regularity theory for optimal transport maps between bounded open sets with -boundary. Our main result asserts sharp $C^{…
Navier-Stokes equations in a curved thin domain, Part III: thin-film limit
Tatsu-Hiko Miura
We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions w…