# Invariances in variance estimates

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Let A = D + B be a block r ï¿½ r, r = 2, Hermitian matrix of order n, where D is the block diagonal part of A. The main results of the paper are Theorems 2.1 and 2.2, which state the sharp inequalities and analyze the equality cases. Some implications of these results are indicated. As...

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We show that any cyclically symmetric monopole is gauge equivalent to Nahm data given by Sutcliffe's ansatz, and so obtained from the affine Toda equations. Further the direction (the Ercolani-Sinha vector) and base point of the linearising flow in the Jacobian of the spectral curve associated...