  We report simulation results of skyrmions on fluctuating 2D lattices, where
the vertices ${\bf r}_i (\in {\bf R}^3)$ are treated as a dynamical variable
and, hence, there is no crystalline structure. On the fluctuating surfaces, an
external magnetic field perpendicular to the surface, Dzyaloshinskii-Moriya and
ferromagnetic interactions are assumed in addition to the Helfrich-Polyakov
Hamiltonian for membranes. The surface (or frame) tension $\tau$ is calculated
under both isotropic and uniaxial strain conditions, and this calculation
clarifies a non-trivial dependence of $\tau$ on the skyrmion, stripe, and
ferromagnetic phases. We find that the variation of $\tau$ with respect to the
applied magnetic field in the skyrmion phase is accompanied by a variation of
the total number of skyrmions. Moreover, we find that this total number
variation is qualitatively consistent with a recent experimental result for the
creation/annihilation of skyrmions of 3D crystalline material under uniaxial
stress conditions. It is also found that the stripe phase is significantly
influenced by uniaxial strains, while the skyrmion phase remains unchanged.
These results allow us to conclude that the skyrmion phase is stable even on
fluctuating surfaces.
