We give a simple, short, and easy proof to the Masaoka theorem that if Dirichlet finiteness and boundedness for harmonic functions on a Riemann surface coincide with each other, then the dimension of the linear space of Dirichlet finite harmonic functions on the Riemann surface and the dimension of the linear space of bounded harmonic functions on the Riemann surface are finite and identical. The essence of our proof lies in the observation that the former of the above two Banach spaces is reflexive while the latter is not unless it is of finite dimension.

In this paper, we give examples of Kirchhoff rod centerlines fully immersed in higher-dimensional space forms. More precisely, we prove that any helix in a space form is a Kirchhoff rod centerline. These examples imply the difference of the geometric properties between Kirchhoff rod centerlines and elasticae.

In a previous work with Thorbergsson, it was proved that a simple closed curve in the real projective plane $\mathbf{P}^{2}$ that is not null-homotopic has at least three sextactic points. This assertion was conjectured by Gerrit Bol. That proof used an axiomatic approach called ‘intrinsic conic system’. The purpose of this paper is to give a more elementary proof.

The purpose of this paper is to prove a conjecture in Yoshida’s book [2, p.33] on the higher derivative of Shintani zeta functions at $s=0$. We use multivariable Shintani zeta functions to prove the conjecture.