3 results
Non-extendable Zero Sets of Harmonic and Holomorphic Functions
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- Journal:
- Canadian Mathematical Bulletin / Volume 59 / Issue 2 / 01 June 2016
- Published online by Cambridge University Press:
- 20 November 2018, pp. 303-310
- Print publication:
- 01 June 2016
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In this paper we study the zero sets of harmonic functions on open sets in
${{\mathbb{R}}^{N}}$ and holomorphic functions on open sets in 
${{\mathbb{C}}^{N}}$. We show that the non-extendability of such zero sets is a generic phenomenon.
Quaternionic Dolbeault complex and vanishing theorems on hyperkähler manifolds
- Part of
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- Journal:
- Compositio Mathematica / Volume 143 / Issue 6 / November 2007
- Published online by Cambridge University Press:
- 01 November 2007, pp. 1576-1592
- Print publication:
- November 2007
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Let (M,I,J,K) be a compact hyperkähler manifold,
, and L a non-trivial holomorphic line bundle on (M,I). Using the quaternionic Dolbeault complex, we prove the following vanishing theorem for holomorphic cohomology of L. If c1(L) lies in the closure 
of the dual Kähler cone, then Hi(L)=0 for i>n. If c1(L) lies in the opposite cone 
, then Hi(L)=0 for i<n. Finally, if c1(L) is neither in nor in , then Hi(L)=0 for 
.
, and 
of the dual Kähler cone, then 
, then 
.Mittag-Leffler Theorems on Riemann Surfaces and Riemannian Manifolds
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- Journal:
- Canadian Journal of Mathematics / Volume 50 / Issue 3 / 01 June 1998
- Published online by Cambridge University Press:
- 20 November 2018, pp. 547-562
- Print publication:
- 01 June 1998
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