Conformal mapping reduces boundary unique continuation and critical point counts for harmonic functions in planar domains to interior nodal set estimates, proving non-vanishing gradient a.e. on boundary for chord arc domains and finite critical points for C1 Dini domains.
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Boundary unique continuation in planar domains by conformal mapping
Conformal mapping reduces boundary unique continuation and critical point counts for harmonic functions in planar domains to interior nodal set estimates, proving non-vanishing gradient a.e. on boundary for chord arc domains and finite critical points for C1 Dini domains.