# Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics

Journal of the European Mathematical Society (2010)

- Volume: 012, Issue: 6, page 1429-1451
- ISSN: 1435-9855

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topTopping, Peter. "Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics." Journal of the European Mathematical Society 012.6 (2010): 1429-1451. <http://eudml.org/doc/277449>.

@article{Topping2010,

abstract = {By exploiting Perelman’s pseudolocality theorem, we prove a new compactness theorem for Ricci flows. By optimising the theory in the two-dimensional case, and invoking the theory of
quasiconformal maps, we establish a new existence theorem which generates a Ricci flow starting at an arbitrary incomplete metric, with Gauss curvature bounded above, on an arbitrary surface. The criterion we assert for well-posedness is that the flow should be complete for all positive times; our discussion of uniqueness also invokes pseudolocality.},

author = {Topping, Peter},

journal = {Journal of the European Mathematical Society},

keywords = {quasiconformal maps; pseudolocality; initial metric of bounded curvature; complete flow; quasiconformal maps; pseudolocality; initial metric of bounded curvature; complete flow},

language = {eng},

number = {6},

pages = {1429-1451},

publisher = {European Mathematical Society Publishing House},

title = {Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics},

url = {http://eudml.org/doc/277449},

volume = {012},

year = {2010},

}

TY - JOUR

AU - Topping, Peter

TI - Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics

JO - Journal of the European Mathematical Society

PY - 2010

PB - European Mathematical Society Publishing House

VL - 012

IS - 6

SP - 1429

EP - 1451

AB - By exploiting Perelman’s pseudolocality theorem, we prove a new compactness theorem for Ricci flows. By optimising the theory in the two-dimensional case, and invoking the theory of
quasiconformal maps, we establish a new existence theorem which generates a Ricci flow starting at an arbitrary incomplete metric, with Gauss curvature bounded above, on an arbitrary surface. The criterion we assert for well-posedness is that the flow should be complete for all positive times; our discussion of uniqueness also invokes pseudolocality.

LA - eng

KW - quasiconformal maps; pseudolocality; initial metric of bounded curvature; complete flow; quasiconformal maps; pseudolocality; initial metric of bounded curvature; complete flow

UR - http://eudml.org/doc/277449

ER -

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