2,238 research outputs found
Weighted interpolation from certain singular affine hypersurfaces
We prove that square integrable holomorphic functions (with respect to a
plurisubharmonic weight) can be extended in a square integrable manner from
certain singular hypersurfaces (which include uniformly flat, normal crossing
divisors) to entire functions in affine space. This provides evidence for a
conjecture regarding the positivity of the curvature of the weight under
consideration.Comment: 7 page
A note on the deformed Hermitian Yang-Mills PDE
We prove a priori estimates for a generalised Monge-Amp\`ere PDE with
"non-constant coefficients" thus improving a result of Sun in the K\"ahler
case. We apply this result to the deformed Hermitian Yang-Mills (dHYM) equation
of Jacob-Yau to obtain an existence result and a priori estimates for some
ranges of the phase angle assuming the existence of a subsolution. We then
generalise a theorem of Collins-Sz\`ekelyhidi on toric varieties and use it to
address a conjecture of Collins-Jacob-Yau.Comment: Final version. 14 pages. To appear in Complex Variables and Elliptic
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