Supercritical conformal metrics on surfaces with conical singularities

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Ricci flow on surfaces with conic singularities (2013, methodology): “f these soliton solutions. The variational approach has recently been extended considerably through the work of Malchiodi et al. to allow angles bigger than 2π, even when coercivity fails, see, e.g., [5, 6, 27]. An extension of our regularity result, Theorem 1.3, also holds for such angles, but our ”
An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, methodology): “The latter existence result was later generalized in [4], [5] to the case of arbitrarily large (but positive) values of ρ.”
Conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces (2013, background): “After this paper was accepted, the authors learned that Daniele Bartolucci, Francesca De Marchis and Andrea Malchiodi [Bartolucci et al. 2011] proved a general existence result for the problem of prescribing the Gaussian curvature on surfaces of positive genus with conical singularities in supercrit”