https://neckpinch.com/authors/satoshi-yokoyama/New arXiv papers by Satoshi Yokoyama, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1811.04265/arxiv:1811.04265Sat, 10 Nov 2018 00:00:00 GMTSatoshi Yokoyama — We study the motion of the hypersurface (γₜ)_(t≥ 0) evolving according to the mean curvature perturbed by w^Q, the formal time derivative of the Q-Wiener process w^Q, in a two dimensional bounded domain. Namely, we consider the equation describing the evolution of γₜ as a stochastic partial differential equation (SPDE) with a multiplicative noise in the Stratonovich sense, whose inward velocity V is determined by V=κ + G ∘ w^Q, where κ is the mean curvature and G is a function determined from γₜ. Already known results in which the noise depends on only time variable is not applicable to our equation. To construct a local solution of the equation describing γₜ, we will derive a certain second order quasilinear SPDE with respect to the signed distance function determined from γ₀. Then we construct the local solution making use of probabilistic tools and the classical Banach fixed-point theorem on suitable Sobolev spaces.Mean curvature flowSurfaces