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Harmonic Maps Between Surfaces and Teichmüller Theory - Lecture 1
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- 1 Start
- 2 Harmonic Maps between surfaces and
- 3 Outline
- 4 Harmonic maps
- 5 A map u0 which is critical for the energy functional Eu
- 6 Example
- 7 Equation
- 8 Example
- 9 Remark
- 10 How to think about harmonicity?
- 11 Applications
- 12 Application of chain rule
- 13 Example: if M is a surface, N=R
- 14 Conclusion
- 15 II. Harmonic maps between surfaces
- 16 How to compare
- 17 Hopf differential
- 18 How does H relate to ϕ?
- 19 Remarks: This is a friendly PDE
- 20 What can we learn about 0H?
- 21 Note
- 22 Picture of Teichmuller space Teich S
- 23 From the perspective of teichmuller space
- 24 Q&A
