• East Asian mathematical journal
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• v.31 no.3
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• pp.351-356
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• 2015

In this paper, we study holomorphic discs in a domain with a plurisubharmonic peak function at a boundary point. The aim is to describe boundary behavior of holomorphic discs in convex finite type domains in the complex Euclidean space in term of a special local neigh-borhood system at a boundary point.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.423-434
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• 2003

We prove an approximation result, and we get a new proof of the main result in [7]. I hope that this new proof may be a step towards a generalization of the Poletsky theory of discs to the case of almost complex manifolds.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1427-1442
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• 2008

We provide another proof that the signed count of the real J-holomorphic spheres (or J- holomorphic discs) passing through a generic real configuration of k points is independent of the choice of the real configuration and the choice of J, if the dimension of the Lagrangian submanifold L (fixed point set of involution) is two or three, and also if we assume L is orient able and relatively spin. We also assume that M is strongly semi-positive. This theorem was first proved by Welschinger in a more general setting, and we provide more natural approach using the signed degree of an evaluation map.

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.629-639
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• 2003

We give results describing behavior of regions of holomorphic extension of CR functions near boundary points of their domain of definition.