Relative metric estimates near reducible Yang–Mills connections
Year: 2026
Type: preprint
Abstract: We study the natural L2 metric near a central Yang–Mills connection on a closed surface. In the classical quadratic symplectic model, we prove a relative metric estimate with error quadratic in the harmonic deformation parameter, uniformly across all stabilizer types. We also compute the leading metric correction using the Green operators of the reference connection. The proof first eliminates the gauge directions with a fixed positive spectral gap and then minimizes over the remaining finite-dimensional orbit; it requires no lower bound on a positive orbit eigenvalue. The same argument compares every small eigenvalue of the gauge Laplacian with the infinitesimal stabilizer-action operator, including at changes of kernel dimension. As a curved finite-dimensional comparison, quaternionic projective and hyperbolic reductions admit exact orbit-metric formulas on their flat moment-map zero cone. A four-cycle is realized in both settings with independently vanishing weights. The resulting estimates distinguish uniform control of the quotient metric from estimates that depend on the smallest orbit scale.
Author: Wuebben, Bernd Johannes
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224092561