MATH 4550: Applicable Geometry
Problem Set 5
Due at 2:54pm before class starts on February 28, 2013
You are allowed to work in groups, but the solutions you hand in should be written by you
only. If you work in a group, you must write the names of your co
arXiv:1501.01291v2 [math.DG] 13 Feb 2015
HEAT KERNEL AND CURVATURE BOUNDS IN RICCI FLOWS
WITH BOUNDED SCALAR CURVATURE
RICHARD H. BAMLER AND QI S. ZHANG
Abstract. In this paper we analyze Ricci flows on which the scalar curvature is globally
or locally bo
Comparison Geometry for the Bakry-Emery Ricci Tensor
Guofang Wei
Will Wylie
Abstract
For Riemannian manifolds with a measure (M, g, ef dvolg ) we prove mean curvature and
volume comparison results when the -Bakry-Emery Ricci tensor is bounded from below a
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What Is Curvature?
If you've just completed an introductory course on dierential geometry,
you might be wondering where the geometry went. In most people's experience, geometry is concerned with properties such as dis
MATH 4550: Applicable Geometry
Problem Set 1
Due at 2:54pm before class starts on January 31, 2013
You are allowed to work in groups, but the solutions you hand in should be written by you
only. If you work in a group, you must write the names of your col
be n elements of Rd written as column vectors. Prove that x1 , . . . , xn are anely
independent if and only if
1
1
x 1 ,1
x1,n
x1 = . , . . . , xn = .
.
.
.
.
xd,1
xd,n
are linearly independent in Rd+1 .
.
P5* (extra credit) Prove that there exists a
MATH 4550: Applicable Geometry
Problem Set 2
Due at 2:54pm before class starts on February 7, 2013
You are allowed to work in groups, but the solutions you hand in should be written by you
only. If you work in a group, you must write the names of your col
MATH 4550: Applicable Geometry
Problem Set 3
Due at 2:54pm before class starts on February 14, 2013
You are allowed to work in groups, but the solutions you hand in should be written by you
only. If you work in a group, you must write the names of your co
MATH 4550: Applicable Geometry
Problem Set 4
Due at 2:54pm before class starts on February 21, 2013
You are allowed to work in groups, but the solutions you hand in should be written by you
only. If you work in a group, you must write the names of your co
The University of Melbourne,
Department of Mathematics and Statistics
Hamiltons Ricci Flow
Nick Sheridan
Supervisor: Associate Professor Craig Hodgson
Second Reader: Professor Hyam Rubinstein
Honours Thesis, November 2006.
Abstract
The aim of this project