Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem

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The legacy of Vladimir Andreevich Steklov (2014, background): “Some bounds were obtained in [11], [29], [18], [21] in terms of the genus and the number of boundary components.”
Upper bounds for Steklov eigenvalues on surfaces (2012, methodology): “In particular, a number of recent papers are concerned with the Steklov spectrum on manifolds with boundary [9, 10, 14, 7].”
SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM (2014, unknown): “Hassannezhad [57], using a generalization of the Korevaar method in combination with concentration results from [22].”
An isoperimetric inequality for Laplace eigenvalues on the sphere (2017, unknown): “For higher eigenvalues, Hassannezhad [22], building on the earlier work of Korevaar [33], proved that there exists a constant C such that for any i > 0 and any compact surface M of genus γ , the following upper bound holds: ¯ λ i ( M, g ) 6 C ( γ + i ) .”