Geometric Evolution of Hypersurfaces Driven by Mean Curvature Flow and Surgical Singularity Analysis - VOLUME 1-41

This 41-volume monograph series by Dr. Zephyrus Thorne rigorously establishes the global existence of Mean Curvature Flow with surgery for high-dimensional hypersurfaces, extending classical 2-convex theory to transfinite time horizons where surgery times accumulate. The work resolves the "Zeno phenomenon" of infinite surgeries by constructing weak Brakke flow limits at accumulation points, utilizing a novel renormalized entropy functional to ensure stability and prevent topological degeneration. By integrating advanced frameworks such as derived moduli stacks, microlocal sheaf theory, and spectral sequences, the series classifies generic singularities and proves Canonical Neighborhood Theorems for non-convex initial data. Key analytic results include the spectral rigidity of self-shrinkers and the quantitative stratification of the singular set, demonstrating that spacetime singularities have a Hausdorff dimension of at most (n-2) across the flow. Ultimately, the project provides a complete topological classification of the initial manifolds, proving they decompose into finite collections of spheres and generalized cylinders, confirming the Generalized Smale Conjecture for specific classes of hypersurfaces.