Related papers: Vanishing and injectivity theorems for LMMP

This preprint has been withdrawn. It is because I will never publish this preprint since everything has been contained in my new preprint: arXiv:0907.1506. Please refer to arXiv:0907.1506. Please do not cite this preprint any more.

This paper has been withdrawn, because it is subsumed by the new preprint arXiv:0806.4540 .

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This paper has been withdrawn. (Reason) Its contents have been entirely superseded by the contents of the articles arXiv:0809.3444 and arXiv:0705.3070. There is no profitable reason to keep it alive. No material on it is however wrong.

This paper has been withdrawn by the author because overcame by arXiv:0910.4694

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This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576

This paper has been withdrawn. The contents of this paper can now be found in 0907.3000, which combines the erstwhile 0901.2981 and 0901.2982 in a somewhat compact form.

This paper has been withdrawn by the author due to an extended and largely modified version of the paper was published in arXiv (see arXiv:0807.3694, Disjoint minimal graphs).

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This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.

This paper has been withdrawn by the author, due to the insecurity against attacks received in quant-ph/0605027v5.

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This paper has been withdrawn by the author(s). Please see arXiv:0711.3910 for revision.

This paper has been withdrawn by the authors.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.

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This paper has been withdrawn.

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