31E05 Potential theory on fractals and metric spaces

Overview

31E05 studies potential theory on fractals and metric spaces in potential theory on fractals and metric spaces. It studies potential-theoretic methods on fractals and metric spaces where classical smooth structure is absent.

Related Wikipedia Page

Potential Theory On Fractals And Metric Spaces (Wikipedia)

Useful Links

• Potential Theory On Fractals And Metric Spaces (Wikipedia)
• Potential theory (Wikipedia)
• Fractal (Wikipedia)

Key Ideas

• Canonical formulations and representative examples for potential theory on fractals and metric spaces
• How structural, local, and computational viewpoints interact in the subject
• Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in analysis on rough spaces, resistance forms, and fractal diffusion.

Applications

• Analysis on fractals
• Resistance forms and Laplacians
• Metric-space potential theory

References

• Kigami, J. (2001) Analysis on Fractals. Cambridge: Cambridge University Press.
• Heinonen, J. (2001) Lectures on Analysis on Metric Spaces. New York, NY: Springer.

Recommended Textbooks

• Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill.
• Topic-focused textbook search (n.d.) Potential theory on fractals and metric spaces. Available via Amazon search.