Global Convergence of the Curvature Flow on Compact Hyperbolic Surfaces
Year: 2026
Type: preprint
Abstract: This work studies a curvature flow in the conformal class of compact hyperbolic surfaces. The main theorem proves that the flow is globally defined for every admissible initial datum and converges to the unique constant-curvature metric in the class. In addition to global existence and convergence in H², the paper establishes eventual exponential decay. The argument combines global a priori bounds, elliptic bootstrap, classification of critical points via holomorphic vector field obstruction, and a spectral gradient inequality based on the Jacobi operator.
Author: Thimoteo, Mário César Garms
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7153843653
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