Weak Laplacian Bounds and Minimal Boundaries in Non-smooth Spaces with Ricci Curvature Lower Bounds

Andrea Mondino, University of Oxford, United Kingdom. Daniele Semola, University of Oxford, United Kingdom

• Chapters;1. Introduction and Main Results; 2. Differential Identities and Overview of the Proofs;3. Analysis of $\theta $-functions; 4. Analysis of the Riemann-Hilbert Problem for $Y$; 5. The Main Parametrix;6. Local Parametrices; 7. Solving the Small Norm Problem;8. Ratio Asymptotics for Non-singular Symbols; 9. Ratio Asymptotics for Fisher-Hartwig Symbols; 10. Partition Function Asymptotics for the $k$-cut Chebyshev Potential; 11. Partition Function Asymptotics