11 citations · 20 across the 9 of their papers we have counts for
9 papers
Strict power concavity of a convolution
Jun O'Hara, Shigehiro Sakata
We give a sufficient condition for the strict parabolic power concavity of the convolution in space variable of a function defined on and a functi…
Movement of time-delayed hot spots in Euclidean space for special initial states
Shigehiro Sakata, Yuta Wakasugi
We consider the Cauchy problem for the damped wave equation under the initial state that the sum of an initial position and an initial velocity vanishes. When the initial position…
Stationary radial centers and characterization of convex polyhedrons
Shigehiro Sakata
We investigate centers of a body (the closure of a bounded open set) defined as maximum points of potentials. In particular, we study centers defined by the Riesz potential and by…
Geometric estimation of a potential and cone conditions of a body
Shigehiro Sakata
We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior c…
Experimental investigation on the uniqueness of a center of a body
Shigehiro Sakata
The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in Rm. Wh…
Movement of time-delayed hot spots in Euclidean space
Shigehiro Sakata, Yuta Wakasugi
We investigate the shape of the solution of the Cauchy problem for the damped wave equation. In particular, we study the existence, location and number of spatial maximizers of the…
Extremal problems for the central projection
Shigehiro Sakata
We consider a projection from the center of the unit sphere to a tangent space of it, the central projection, and study two area minimizing problems of the image of a closed subset…
Extremal problems for the solid angle
Shigehiro Sakata
We consider the solid angle that a planar compact subset subtends at a point in a level set of height h and study two extremal problems for the solid angle. One of the variables is…
Space of subspheres and conformal invariants of curves
R. Langevin, J. O'Hara, S. Sakata
A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to Möbius transformations. We use the spaces of osculating circles and spheres t…