Preprint: Solutions of stationary McKean–Vlasov equation on a high-dimensional sphere and other Riemannian manifolds
Together with Anna Shalova, we study stationary solutions of McKean-Vlasov equation on a high-dimensional sphere and other compact Riemannian manifolds. We extend the equivalence of the energetic problem formulation to the manifold setting and characterize critical points of the corresponding free energy functional. On a sphere, we employ the properties of spherical convolution to study the bifurcation branches around the uniform state. We also give a sufficient condition for an existence of a discontinuous transition point in terms of the interaction kernel and compare it to the Euclidean setting.
Now published in Adv. Nonlinear Anal. 15(1), 20250141 (2026).
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