Related papers: On the paper "The Payne conjecture for Dirichlet a…

We prove the long-standing Payne conjecture that the $k^{\text{th}}$ eigenvalue in the buckling problem for a clamped plate is not less than the ${k+1}^{\text{st}}$ eigenvalue for the membrane of the same shape which is fixed on the…

The paper has been withdrawn by the author due to a crucial error.

A celebrated inequality by Payne relates the first eigenvalue of the Dirichlet Laplacian to the first eigenvalue of the buckling problem. Motivated by the goal of establishing a quantitative version of this inequality, we show that Payne's…

The original version of this paper contains an error; when this is corrected the basic conclusion changes. A revised manuscript will be submitted shortly.

The paper is devoted to description of two interconnected mistakes generated by the gap in the Du and Hwang approach to Gilbert-Pollack Steiner ratio conjecture.

There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.

Withdrawn. We thank J. T. Liu for bringing an error in the manuscript to our attention.

The purpose of this note is to correct an error in a paper of M. Cowling, G. Fendler and J.J.F. Fournier, and to give a counterexample to a conjecture of J.-L. Rubio de Francia.

This manuscripts corrects some minor error in the paper, Mod. Phys. Lett. A 6 1893 (1991)

This paper has been withdrawn by the author, due to a crucial error in page 5.

In this note, we correct an oversight from the paper mentioned in the title.

We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional…

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

This is a correction to the afore-mentioned paper in Duke Math. J. vol. 75 (1994), 99-119 by S. Keel, K. Matsuki, and J. McKernan. We completely rewrite Chapter 6 according to the original manuscript of the second author, in order to fix…

This paper has been withdrawn by the author due to a crucial error.

In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.

A very short note, explaining the error in the original paper, which renders its central result incorrect.

The purpose of this paper was to give an algebraic analog of Poincare duality. But there is a mistake in the proof of the main theorem. It will be corrected as soon as possible.

This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)

This paper has been withdrawn by the author due to a crucial argument error at p.10.