Skip to content
Register Sign in Wishlist

Geometric Analysis

Part of Cambridge Studies in Advanced Mathematics

  • Author: Peter Li, University of California, Irvine
  • Date Published: May 2012
  • availability: Available
  • format: Hardback
  • isbn: 9781107020641

Hardback

Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

Please email academicmarketing@cambridge.edu.au to enquire about an inspection copy of this book

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • The aim of this graduate-level text is to equip the reader with the basic tools and techniques needed for research in various areas of geometric analysis. Throughout, the main theme is to present the interaction of partial differential equations and differential geometry. More specifically, emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the underlying manifold and vice versa. For efficiency the author mainly restricts himself to the linear theory and only a rudimentary background in Riemannian geometry and partial differential equations is assumed. Originating from the author's own lectures, this book is an ideal introduction for graduate students, as well as a useful reference for experts in the field.

    • Originates from the author's lectures to graduate students
    • A short treatment of the heat equation provides background for research in geometric flows
    • The tools presented here can also be used in nonlinear theory
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: May 2012
    • format: Hardback
    • isbn: 9781107020641
    • length: 418 pages
    • dimensions: 229 x 152 x 28 mm
    • weight: 0.73kg
    • availability: Available
  • Table of Contents

    Introduction
    1. First and second variational formulas for area
    2. Volume comparison theorem
    3. Bochner–Weitzenböck formulas
    4. Laplacian comparison theorem
    5. Poincaré inequality and the first eigenvalue
    6. Gradient estimate and Harnack inequality
    7. Mean value inequality
    8. Reilly's formula and applications
    9. Isoperimetric inequalities and Sobolev inequalities
    10. The heat equation
    11. Properties and estimates of the heat kernel
    12. Gradient estimate and Harnack inequality for the heat equation
    13. Upper and lower bounds for the heat kernel
    14. Sobolev inequality, Poincaré inequality and parabolic mean value inequality
    15. Uniqueness and maximum principle for the heat equation
    16. Large time behavior of the heat kernel
    17. Green's function
    18. Measured Neumann–Poincaré inequality and measured Sobolev inequality
    19. Parabolic Harnack inequality and regularity theory
    20. Parabolicity
    21. Harmonic functions and ends
    22. Manifolds with positive spectrum
    23. Manifolds with Ricci curvature bounded from below
    24. Manifolds with finite volume
    25. Stability of minimal hypersurfaces in a 3-manifold
    26. Stability of minimal hypersurfaces in a higher dimensional manifold
    27. Linear growth harmonic functions
    28. Polynomial growth harmonic functions
    29. Lq harmonic functions
    30. Mean value constant, Liouville property, and minimal submanifolds
    31. Massive sets
    32. The structure of harmonic maps into a Cartan–Hadamard manifold
    Appendix A. Computation of warped product metrics
    Appendix B. Polynomial growth harmonic functions on Euclidean space
    References
    Index.

  • Instructors have used or reviewed this title for the following courses

    • Topics in Geometric Analysis
    • advance mathematics for computer vision and robotics
  • Author

    Peter Li, University of California, Irvine
    Peter Li is Chancellor's Professor at the University of California, Irvine.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×