We characterize the conjugate linearized Ricci flow and the associated backward heat kernel on closed three-manifolds of bounded geometry. We discuss their properties, and introduce the notion of Ricci flow conjugated constraint sets which characterizes a way of Ricci flow averaging metric dependent geometrical data. We also provide an integral representation of the Ricci flow metric itself and of its Ricci tensor in terms of the heat kernel of the conjugate linearized Ricci flow. These results, which readily extend to closed $n$-dimensional manifolds, yield various conservation laws, monotonicity and asymptotic formulas for the Ricci flow and its linearization.

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@article{ASNSP_2009_5_8_4_681_0, author = {Carfora, Mauro}, title = {The conjugate linearized {Ricci} flow on closed 3-manifolds}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {681--724}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 8}, number = {4}, year = {2009}, zbl = {1190.53067}, mrnumber = {2647909}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2009_5_8_4_681_0/} }

TY - JOUR AU - Carfora, Mauro TI - The conjugate linearized Ricci flow on closed 3-manifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 DA - 2009/// SP - 681 EP - 724 VL - Ser. 5, 8 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2009_5_8_4_681_0/ UR - https://zbmath.org/?q=an%3A1190.53067 UR - https://www.ams.org/mathscinet-getitem?mr=2647909 LA - en ID - ASNSP_2009_5_8_4_681_0 ER -

Carfora, Mauro. The conjugate linearized Ricci flow on closed 3-manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 4, pp. 681-724. http://www.numdam.org/item/ASNSP_2009_5_8_4_681_0/

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