Inverse Hessian Curvature Flow in Minkowski Space II: The Dirichlet problem at infinity

What the math gives to ML

The paper formulates a geometric self-shrinker as a fully nonlinear elliptic equation on hyperbolic space, using the eigenvalues of the shifted Hessian \(\nabla^2v-vg\). Its transferable asset is a differentiable curvature-cone constraint combined with a scale-normalized symmetric-polynomial residual and boundary conditioning at infinity. This can become a hyperbolic neural-field loss that encourages structured, convex latent representations and stable extrapolation rather than unconstrained interpolation. The most direct test is a small physics-informed or implicit-representation model trained on the hyperbolic Dirichlet residual and compared with Euclidean Hessian regularization.