1547845447-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_IV__Chow_

CONTENTS vii

• Chapter 27. Noncompact Gradient Ricci Solitons Notation and Symbols xvii
  
  
  • l. Basic properties of gradient Ricci solitons
  
  
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    2. Estimates for potential functions of gradient so litons
    
    
    
    
    
    
    • gradient Ricci solitons 3. Lower bounds for t he scalar curvature of nonflat nonexpanding
    
    
    
    
  
  
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    4. Volume growth of shrinking gradient Ricci solitons
    
    
    
    
  
  
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    5. Logarithmic Sobolev inequality
    
    
    
    
  
  
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    6. Gradient shrinkers with nonnegative Ricci curvature
    
    
    
    
  
  
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    7. Notes and commentary
    
    
    
    
  
  
  
  


• Chapter 28. Special Ancient Solutions
  
  
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    1. Local estimate for the scalar curvature under Ricci flow
    
    
    
    
  
  
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    2. Properties of singularity models
    
    
    
    
  
  
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    3. Noncompact 2-dimensional ancient solut ions with finite width
    
    
    
    
  
  
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    4. Ancient solutions with positive curvature
    
    
    
    
  
  
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    5. Notes and commentary
    
    
    
    
  
  
  
  


• Chapter 29. Compact 2-Dimensional Ancient Solutions
  
  
  • l. Statement of the classification result and outline of its proof
  
  
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    2. The Ricci flow equation on 52 and some intuition
    
    
    
    
  
  
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    3. The King- Rosenau solution in the various coordinates
    
    
    
    
  
  
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    4. A priori estimates for the pressure function
    
    
    
    
  
  
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    5. The almost everywh ere vanishing of R
    
    
    
    
  
  
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    6. First properties of the backward limit v
    
    
    
    
  
  
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    7. Isoperimetric co nstant of metrics on
    
    
    
    
  
  
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    8. Characterizing round solutions
    
    
    
    
  
  
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    9. Classifying the backward pointwise limit
    
    
    
    
  
  
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    10. An unrescaled cigar backward Cheeger- Gromov limit
    
    
    
    
  
  
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    11. Irreducible components of \7^3 v
    
    
    
    
  
  
  • 12 The heat-type equation satisfied by Q
  
  
  • 13 That Q = 0 implies the solution is t he King- Rosenau solution
  
  
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    14. The evolution equation for Q
    
    
    
    
  
  
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    15. The quantity Q must be identically zero
    
    
    
    
  
  
  • Chapter 36. Type II Singularities and Degenerate Neckpinches
    
    
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      1. Numerical simulation of solutions with degenerate neckpinches
      
      
      
      
    
    
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      2. Matched asymptotic studies of degenerate neckpinches
      
      
      
      
    
    
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      3. Ricci flow solutions with degenerate neckpinch singularities
      
      
      
      
    
    
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      4. Concluding remarks
      
      
      
      
    
    
    
    
  
  
  • Appendix K. Implicit Function Theorem
    
    
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      1. The implicit function theorem
      
      
      
      
    
    
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      2. Holder spaces and Sobolev spaces on manifolds
      
      
      
      
    
    
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      3. Harmonic maps and their linearization
      
      
      
      
    
    
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      4. Spectrum of 6.d on p-forms on sn
      
      
      
      
    
    
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      5. Notes and commentary
      
      
      
      
    
    
    
    
  
  
  • Bibliography
  
  
  
  


• Index