Riku Kishida

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20242026

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math.DG2026

A new framework of zero mean curvature surfaces in the isotropic 3-space

Riku Kishida

We introduce a class of zero mean curvature surfaces with singularities in the isotropic 3-space, called ZMC-faces. As a main result, we establish three Osserman-type inequalities…

math.DG2025

The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition

Riku Kishida

In this paper, we focus on a marginally trapped submanifold $f : I^£^{n} \to M_{1}^{n + 2}$ in a Lorentzian manifold $M_{1}^{n + 2}$ . We show that $f$ lies in a certain null hypersurface $\mathc…

math.DG2024

The volume of conformally flat manifolds as hypersurfaces in the light-cone

Riku Kishida

In this paper, we focus on a conformally flat Riemannian manifold $(M^{n}, g)$ of dimension $n$ isometrically immersed into the $(n + 1)$ -dimensional light-cone $I^^{n + 1}$ as a hypersur…