Related papers: Geometric Auslander criterion for flatness

This paper was withdrawn by the author.

This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.

The paper has been withdrawn because the proof of part (b) of the main theorem is incomplete.

This paper has been withdrawn by the author.

The author decided to withdraw this paper by 1) an error in Lemma 5.11 (and 5.12) which requires some justification; 2) the main result of this paper suffers overlap with arXiv:1203.5254; 3) the author decided to split arXiv:1203.5254 into…

The paper has been withdrawn by the authors for modification.

This paper has been withdrawn as the proof of Lemma 4.1 is incomplete.

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn, because its material has been revised and became part of paper math.GT/0010184

This paper has been withdrawn due to an error in section 3.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

Flatness of a plate is a parameter has been put under consideration for long time. Factors influencing the accuracy of this parameter have been recognized and examined carefully but placed scatterringly. Beside that those reports have not…

The paper has been withdrawn.

The paper is withdrawn.

This paper has been withdrawn.

This paper has been withdrawn by the author due to a crucial definition error of Triebel space.

The paper has been withdrawn due to an error in the main theorem.

This paper has been withdrawn.

This paper has being withdrawn by the authors due to an error in the conclusion.

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.