Related papers: A note on symplectic rational blow--downs

This paper has been withdrawn by the authors due to inadequate arguments.

The paper has been withdrawn by change of content and some errors in the examples.

Harer, Kas and Kirby have conjectured that every handle decomposition of the elliptic surface $E(1)_{2,3}$ requires both 1- and 3-handles. In this article, we construct a smooth 4-manifold which has the same Seiberg-Witten invariant as…

We explain an error in our paper "A smooth foliation of the 5-sphere by complex surfaces", Ann. Math 156 (2002), p.915-930.

This paper has been withdrawn by the author due to an error.

We study polarized cylinders in certain rational surfaces arising from blow-ups of weighted projective planes. In particular, we consider the surfaces obtained by blowing up $m+4$ points in general position on the weighted projective plane…

For a regular mean field equation defined on a compact Riemann surface, an important work of Bartolucci-Jevnikar-Lee-Yang \cite{bart-4} proved a uniqueness theorem for blow-up solutions under non-degeneracy assumptions. However, the proof…

We show that every negative definite configuration of symplectic surfaces in a symplectic 4--manifold has a strongly symplectically convex neighborhood. We use this to show that, if a negative definite configuration satisfies an additional…

The aim of this note is to investigate characterizations and deformations of elliptic Calabi--Yau manifolds, building on earlier works of Wilson and Oguiso. Version 2: References updated and small changes. Version 3: Smoothness conditions…

This paper has been withdrawn by the author. It is not true that plt blow-up of toric singularity is toric (in dimension 3 too) and the first main theorem is incorrect also. The error is in deformation argument. I am grateful to Ivan…

It is shown that the experimentally observed inverse linear decay of surface corrugations in Si(001) (Erlebacher et al., Phys. Rev. Lett. 84, 5800 (2000)) is due to the two dimensional nature of the surface in the experimental system. The…

In this paper, we analyze the blowup behavior of regularized solutions to Jang equation inside apparent horizons. This extends the analyses outside apparent horizons done by Schoen-Yau. We will take two natural geometric treatments to…

No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…

This paper has been withdrawn by the authors.

In this paper we show that if the minimal good resolution graph of a normal surface singularity contains at least two nodes (i.e. vertex with valency at least 3) then the singularity does not admit a smoothing with Milnor fiber having…

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.

This paper has been withdrawn by the author(s) and included into the new version of "An extension theorem for separately holomorphic functions with singularities", math.CV/0104089.

In their work on a sharp compactness theorem for the Yamabe problem, Khuri, Marques and Schoen apply a refined blow-up analysis (what we call `second order blow-up argument' in this article) to obtain highly accurate approximate solutions…

This paper has been withdrawn by the authors. Significantly revised versions of the results of this paper are now available in arXiv:0707.0487v2 and arXiv:0808.3169v1.