Research

Research fields: Convex analysis and geometry

Research objects: Centers of a body, power concave functions, sections of a convex body, maximizers of a function

Publications:

[1] Extremal problems for the central projection, J. Geom. 103 (2012), 125--129.

[2] (with R. Langevin and J. O'Hara) Application of spaces of subspheres to conformal invariants of curves and canal surfaces, Ann. Polon. Math. 108 (2013), no. 2, 109--131.

[3] Movement of centers with respect to various potentials, Trans. Amer. Math. Soc. 367 (2015), 8347--8381.

[4] Experimental investigation on the uniqueness of a center of a body, Ann. Polon. Math. 118 (2016), no. 2--3, 149--171.

[5] (with Y. Wakasugi) Movement of time-delayed hot spots in Euclidean space, Math. Z. 285 (2017) , no. 3--4, 1007--1040.

[6] Geometric estimation of a potential and cone conditions of a body, J. Geom. Anal. 27 (2017), Issue 3, 2155--2189.

[7] Every convex body has a unique illuminating center, J. Geom. 108 (2017), Issue 2, 655--662.

[8] Stationary radial centers and symmetry of convex polytopes, Colloq. Math. 159 (2020), No. 1, 91--106.

[9] (with Y. Wakasugi) Movement of time-delayed hot spots in Euclidean space for a degenerate initial state, Discrete Contin. Dyn. Syst. Ser. A 40 (2020), no. 5, 2705--2738.

[10] (with I. Herburt) An extremum problem for the power moment of a convex polygon contained in a disc, Adv. Geom. 21 (2021), no. 4, 599--609.

[11] Analytic characterization of equilateral triangles, Ann. Mat. Pura Appl. (1923-), 200 (2021), 2191--2212. 

[12] (with J. O'Hara) Strict power concavity of a convolution, Ann. Mat. Pura Appl. (1923-), 201 (2022), 1553--1575.

[13] Euclidean geometric description of radial centers of a triangle, Colloq. Math. 170 (2022), No. 2, 275--288.

[14] Convexity of the radial sum of a star body and a ball, Canad. Math. Bull. 67 (2024), Issue 2, 289--303.

Refereed proceedings:

[1] S. Kaji, S. Hirose, S. Sakata, Y. Mizoguchi and K. Anjyo, Mathematical analysis on affine maps for 2D shapes interpolation, Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2012), 71--76.

Preprint(s):

[1] (with Y. Wakasugi), in preparation.