Related papers: Eigen-value monotonicity for the Ricci-Hamilton fl…
This paper has been withdrawn by the author
This paper has been withdrawn by the authors.
This paper has been withdrawn because it has been by far superseded by the Author's post arXiv:1108.1306v6, which was published on 30/08/2011.
This paper has been withdrawn by the author.
We prove sharp lower bounds for eigenvalues of the drift Laplacian for a modified Ricci flow. The modified Ricci flow is a system of coupled equations for a metric and weighted volume that plays an important role in Ricci flow. We will also…
This paper has been withdrawn by the author
This paper has been withdrawn by the authors.
This paper has been withdrawn by the authors.
In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy functional and the $\mathcal{W}$-functional of Perelman type.
This paper has been withdrawn by the author due to a new work in [arXiv:0901.0456v4] which can contain the results in this paper.
This paper has been withdrawn by the author.
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2080.
This paper has been withdrawn by the authors, as it was combined with "Conformally invariant energies of knots I" (math/0409396) to be "Conformally invariant energies of knots" which has replaced the former.
This paper is withdrawn.
This paper has been withdrawn by the author due to errors.
This paper has been withdrawn by the author.
This paper has been withdrawn by the author due to the inaccurate result.
We derive identities for general flows of Riemannian metrics that may be regarded as local mean-value, monotonicity, or Lyapunov formulae. These generalize previous work of the first author for mean curvature flow and other nonlinear…
This paper has been withdrawn by the author in order to implement the referee's suggestions and comments.