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31Cxx Other generalizations

This subtopic studies other generalizations of potential theory, including abstract and nonclassical settings where classical kernels are generalized.

Specific topics

31C05 Harmonic, subharmonic, superharmonic functions on other spaces

Overview

31C05 studies harmonic, subharmonic, superharmonic functions on other spaces in other generalizations in potential theory. It gathers generalizations of potential theory beyond the classical Euclidean setting, including nonlinear and probabilistic viewpoints.

Related Wikipedia Page

Other Generalizations In Potential Theory (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for harmonic, subharmonic, superharmonic functions on other spaces
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to extend potential-theoretic methods to broader geometric and analytic contexts.

Applications

  • Nonlinear potential theory
  • Probabilistic methods
  • Extensions beyond Euclidean spaces

References

Recommended Textbooks

31C10 Pluriharmonic and plurisubharmonic functions and generalizations

Overview

31C10 studies pluriharmonic and plurisubharmonic functions and generalizations in other generalizations in potential theory. It gathers generalizations of potential theory beyond the classical Euclidean setting, including nonlinear and probabilistic viewpoints.

Related Wikipedia Page

Other Generalizations In Potential Theory (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for pluriharmonic and plurisubharmonic functions and generalizations
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to extend potential-theoretic methods to broader geometric and analytic contexts.

Applications

  • Nonlinear potential theory
  • Probabilistic methods
  • Extensions beyond Euclidean spaces

References

Recommended Textbooks

31C12 Potential theory on Riemannian manifolds and other spaces

Overview

31C12 studies potential theory on riemannian manifolds and other spaces in other generalizations in potential theory. It gathers generalizations of potential theory beyond the classical Euclidean setting, including nonlinear and probabilistic viewpoints.

Related Wikipedia Page

Other Generalizations In Potential Theory (Wikipedia)

Useful Links

Key Ideas

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

Typical Uses

Used to extend potential-theoretic methods to broader geometric and analytic contexts.

Applications

  • Nonlinear potential theory
  • Probabilistic methods
  • Extensions beyond Euclidean spaces

References

Recommended Textbooks

31C15 Potentials and capacities on other spaces

Overview

31C15 studies potentials and capacities on other spaces in other generalizations in potential theory. It gathers generalizations of potential theory beyond the classical Euclidean setting, including nonlinear and probabilistic viewpoints.

Related Wikipedia Page

Other Generalizations In Potential Theory (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for potentials and capacities on other spaces
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to extend potential-theoretic methods to broader geometric and analytic contexts.

Applications

  • Nonlinear potential theory
  • Probabilistic methods
  • Extensions beyond Euclidean spaces

References

Recommended Textbooks

31C20 Discrete potential theory

Overview

31C20 studies discrete potential theory in other generalizations in potential theory. It gathers generalizations of potential theory beyond the classical Euclidean setting, including nonlinear and probabilistic viewpoints.

Related Wikipedia Page

Other Generalizations In Potential Theory (Wikipedia)

Useful Links

Key Ideas

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

Typical Uses

Used to extend potential-theoretic methods to broader geometric and analytic contexts.

Applications

  • Nonlinear potential theory
  • Probabilistic methods
  • Extensions beyond Euclidean spaces

References

Recommended Textbooks

31C25 Dirichlet forms

Overview

31C25 studies dirichlet forms in other generalizations in potential theory. It gathers generalizations of potential theory beyond the classical Euclidean setting, including nonlinear and probabilistic viewpoints.

Related Wikipedia Page

Other Generalizations In Potential Theory (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for dirichlet forms
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to extend potential-theoretic methods to broader geometric and analytic contexts.

Applications

  • Nonlinear potential theory
  • Probabilistic methods
  • Extensions beyond Euclidean spaces

References

Recommended Textbooks

31C35 Martin boundary theory

Overview

31C35 studies martin boundary theory in other generalizations in potential theory. It gathers generalizations of potential theory beyond the classical Euclidean setting, including nonlinear and probabilistic viewpoints.

Related Wikipedia Page

Other Generalizations In Potential Theory (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for martin boundary theory
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to extend potential-theoretic methods to broader geometric and analytic contexts.

Applications

  • Nonlinear potential theory
  • Probabilistic methods
  • Extensions beyond Euclidean spaces

References

Recommended Textbooks

31C40 Fine potential theory; fine topology

Overview

31C40 studies fine potential theory; fine topology in other generalizations in potential theory. It gathers generalizations of potential theory beyond the classical Euclidean setting, including nonlinear and probabilistic viewpoints.

Related Wikipedia Page

Other Generalizations In Potential Theory (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for fine potential theory; fine topology
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to extend potential-theoretic methods to broader geometric and analytic contexts.

Applications

  • Nonlinear potential theory
  • Probabilistic methods
  • Extensions beyond Euclidean spaces

References

Recommended Textbooks