TY - JOUR
T1 - On the number of omitted values by a meromorphic function of finite energy and heat diffusions
AU - Atsuji, Atsushi
PY - 2010/10/1
Y1 - 2010/10/1
N2 - We give a bound of the number of omitted values by a meromorphic function of finite energy on parabolic manifolds in terms of Ricci curvature and the energy of the functions. An analogy of Nevanlinna's theorems based on heat diffusions is used. We also show that meromorphic functions whose energy satisfies some growth condition on algebraic varieties can omit at most two points as a corollary to our main theorems.
AB - We give a bound of the number of omitted values by a meromorphic function of finite energy on parabolic manifolds in terms of Ricci curvature and the energy of the functions. An analogy of Nevanlinna's theorems based on heat diffusions is used. We also show that meromorphic functions whose energy satisfies some growth condition on algebraic varieties can omit at most two points as a corollary to our main theorems.
KW - Brownian motion on Kähler manifolds
KW - Meromorphic function
KW - Nevanlinna theory
KW - Value distribution theory
UR - http://www.scopus.com/inward/record.url?scp=77956267753&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77956267753&partnerID=8YFLogxK
U2 - 10.1007/s12220-010-9131-6
DO - 10.1007/s12220-010-9131-6
M3 - Article
AN - SCOPUS:77956267753
VL - 20
SP - 1008
EP - 1025
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
SN - 1050-6926
IS - 4
ER -