TY - JOUR
T1 - Harnack estimates for conjugate heat kernel on evolving manifolds
AU - Cao, Xiaodong
AU - Guo, Hongxin
AU - Tran, Hung
N1 - Funding Information:
X. Cao was partially supported by a Grant from the Simons Foundation (#280161) and by the Jeffrey Sean Lehman Fund from Cornell University; H. Guo was supported by NSF of China (Grant No. 11171143) and Zhejiang Provincial Natural Science Foundation of China (Project No. LY13A010009).
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2015/10/19
Y1 - 2015/10/19
N2 - In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation provides a unified framework for some known results, in particular including corresponding results of Ni (J Geom Anal 14(1): 87–100, 2004), Perelman (arXiv:math.DG/0211159, 2002) and Tran (arXiv:1211.6448, 2012) as special cases. Moreover, it leads to new results in the setting of Ricci-Harmonic flow and mean curvature flow in Lorentzian manifolds with nonnegative sectional curvature.
AB - In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation provides a unified framework for some known results, in particular including corresponding results of Ni (J Geom Anal 14(1): 87–100, 2004), Perelman (arXiv:math.DG/0211159, 2002) and Tran (arXiv:1211.6448, 2012) as special cases. Moreover, it leads to new results in the setting of Ricci-Harmonic flow and mean curvature flow in Lorentzian manifolds with nonnegative sectional curvature.
KW - Primary 53C44
UR - http://www.scopus.com/inward/record.url?scp=84939567563&partnerID=8YFLogxK
U2 - 10.1007/s00209-015-1479-7
DO - 10.1007/s00209-015-1479-7
M3 - Article
AN - SCOPUS:84939567563
SN - 0025-5874
VL - 281
SP - 201
EP - 214
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1-2
ER -