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Volume 20, Issue 3
Ricci Flow on Surfaces with Degenerate Initial Metrics

Xiuxiong Chen & Weiyue Ding

J. Part. Diff. Eq., 20 (2007), pp. 193-202.

Published online: 2007-08

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  • Abstract

It is proved that given a conformal metric e^{u0}g_0, with e^{u0} ∈ L∞, on a 2-dim closed Riemannian manfold (M, g_0), there exists a unique smooth solution u(t) of the Ricci flow such that u(t) → u_0 in L² as t → 0.

  • Keywords

Ricci flows degenerate metrics on surfaces

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COPYRIGHT: © Global Science Press

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@Article{JPDE-20-193, author = {Xiuxiong Chen and Weiyue Ding }, title = {Ricci Flow on Surfaces with Degenerate Initial Metrics}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {3}, pages = {193--202}, abstract = {

It is proved that given a conformal metric e^{u0}g_0, with e^{u0} ∈ L∞, on a 2-dim closed Riemannian manfold (M, g_0), there exists a unique smooth solution u(t) of the Ricci flow such that u(t) → u_0 in L² as t → 0.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5302.html} }
TY - JOUR T1 - Ricci Flow on Surfaces with Degenerate Initial Metrics AU - Xiuxiong Chen & Weiyue Ding JO - Journal of Partial Differential Equations VL - 3 SP - 193 EP - 202 PY - 2007 DA - 2007/08 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5302.html KW - Ricci flows KW - degenerate metrics on surfaces AB -

It is proved that given a conformal metric e^{u0}g_0, with e^{u0} ∈ L∞, on a 2-dim closed Riemannian manfold (M, g_0), there exists a unique smooth solution u(t) of the Ricci flow such that u(t) → u_0 in L² as t → 0.

Xiuxiong Chen and Weiyue Ding . (2007). Ricci Flow on Surfaces with Degenerate Initial Metrics. Journal of Partial Differential Equations. 20 (3). 193-202. doi:
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