Harmonic Maps Between Surfaces and Teichmüller Theory - Lecture 1
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
Start
Harmonic Maps between surfaces and
Outline
Harmonic maps
A map u0 which is critical for the energy functional Eu
Example
Equation
Example
Remark
How to think about harmonicity?
Applications
Application of chain rule
Example: if M is a surface, N=R
Conclusion
II. Harmonic maps between surfaces
How to compare
Hopf differential
How does H relate to ϕ?
Remarks: This is a friendly PDE
What can we learn about 0H?
Note
Picture of Teichmuller space Teich S
From the perspective of teichmuller space
Q&A
Taught by
International Centre for Theoretical Sciences