NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	THE LELAND STANFORD JUNIOR UNIVERSITY
Initial Amendment Date:	May 2, 2002
Latest Amendment Date:	May 2, 2002
Award Number:	0203023
Award Instrument:	Standard Grant
Program Manager:	Alexandre Freire DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 2002
End Date:	June 30, 2003 (Estimated)
Total Intended Award Amount:	$82,993.00
Total Awarded Amount to Date:	$82,993.00
Funds Obligated to Date:	FY 2002 = $24,302.00
History of Investigator:	Lei Ni (Principal Investigator) lni@math.ucsd.edu
Recipient Sponsored Research Office:	Stanford University 450 JANE STANFORD WAY STANFORD CA  US  94305-2004 (650)723-2300
Sponsor Congressional District:	16
Primary Place of Performance:	Stanford University 450 JANE STANFORD WAY STANFORD CA  US  94305-2004
Primary Place of Performance Congressional District:	16
Unique Entity Identifier (UEI):	HJD6G4D6TJY5
Parent UEI:
NSF Program(s):	GEOMETRIC ANALYSIS
Primary Program Source:	app-0102
Program Reference Code(s):	0000, OTHR
Program Element Code(s):	126500
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

ABSTRACT DMS - 0203023.
PI: Lei Ni

The principle investigator proposes to study the interplay between the
geometry and the analysis on complete Kaehler manifolds. The focus will be
linear and nonlinear analysis on such manifolds. The main tool is solving
the linear equation, such as the Poisson equation and Poincare-Lelong
equation, and the nonlinear equations such as the Kaehle-Ricci flow. The
goal is to understand the space of holomorphic functions (plurisubharmonic
functions), the interplay between the geometry and the function theory and
applying the results to the uniformization of complete Kaehler manifolds
with nonnegative curvature.

The manifold is the space where every physical event happens. The
global analysis on manifolds studies the overall properties of the
manifolds by piecing together the local information. Kaehler manifolds are
the basic block in the universe model according to the
string theory. The proposed study
has close connection with the theory of general relativity and string
theory. The nonlinear differential equations studied in the proposal have
applications in the study of the structure of complicated molecules,
liquid-gas boundary, and even the large scale networks.

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