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On exponential Yang–Mills fields and p-Yang–Mills fields

  • Shihshu Walter Wei
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Geometric Potential Analysis
Ein Kapitel aus dem Buch Geometric Potential Analysis

Abstract

We introduce normalized exponential Yang-Mills energy functional ym0e , stress-energy tensor Se,ym0 associated with the normalized exponential Yang-Mills energy functional yM0e , e-conservation law. We also introduce the notion of the e-degree de which connects two separate parts in the associated normalized exponential stress-energy tensor Se,YM0 (cf. (3.10) and (4.15)), derive monotonicity formula for exponential Yang-Mills fields, and prove a vanishing theorem for exponential Yang-Mills fields. These monotonicity formula and vanishing theorem for exponential Yang-Mills fields augment and extend the monotonicity formula and vanishing theorem for F-Yang-Mills fields in [18] and [68, 9.2]. We also discuss an average principle (cf. Proposition 8.1), isoperimetric and Sobolev inequalities, convexity and Jensen’s inequality, p-Yang-Mills fields, an extrinsic average variational method in the calculus of variation and Φ(3)-harmonic maps, from varied, coupled, generalized viewpoints and perspectives (cf. Theorems 6.1, 7.1, 9.1, 9.2, 10.1, 10.2, 11.13, 11.14, and 11.15).

Abstract

We introduce normalized exponential Yang-Mills energy functional ym0e , stress-energy tensor Se,ym0 associated with the normalized exponential Yang-Mills energy functional yM0e , e-conservation law. We also introduce the notion of the e-degree de which connects two separate parts in the associated normalized exponential stress-energy tensor Se,YM0 (cf. (3.10) and (4.15)), derive monotonicity formula for exponential Yang-Mills fields, and prove a vanishing theorem for exponential Yang-Mills fields. These monotonicity formula and vanishing theorem for exponential Yang-Mills fields augment and extend the monotonicity formula and vanishing theorem for F-Yang-Mills fields in [18] and [68, 9.2]. We also discuss an average principle (cf. Proposition 8.1), isoperimetric and Sobolev inequalities, convexity and Jensen’s inequality, p-Yang-Mills fields, an extrinsic average variational method in the calculus of variation and Φ(3)-harmonic maps, from varied, coupled, generalized viewpoints and perspectives (cf. Theorems 6.1, 7.1, 9.1, 9.2, 10.1, 10.2, 11.13, 11.14, and 11.15).

Kapitel in diesem Buch

  1. Frontmatter I
  2. Foreword V
  3. Contents VII
  4. Hardy spaces associated to the Kohn Laplacian on a family of model domains in Cn+1 1
  5. Affine mixed Rayleigh quotients 29
  6. Riesz potentials and Hardy–Morrey spaces 49
  7. A conjecture regarding compact Lie groups and its consequences 79
  8. The singular Fredholm integral operators and related integral equations of Chandrasekhar type 89
  9. Extended multichannel weighted Schatten p-norm minimization for color image denoising 105
  10. The boundedness of a bilinear oscillatory integral 123
  11. On sharp Sobolev-type inequalities for multidimensional Cauchy measures 135
  12. Banach lattice-valued q-variation and convexity 153
  13. Weighted boundedness of Marcinkiewicz integral operators and related singular integral operators 167
  14. A spectral comparison note 195
  15. On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds 207
  16. The Neumann problem for the Laplacian in half-spaces 219
  17. An inequality on the mass of image of rectifiable chain under Lipschitz map 253
  18. Boundedness of general alternative Gaussian singular integrals on Gaussian variable Lebesgue spaces 261
  19. Remarks on weak–strong uniqueness for two-fluid model 281
  20. Coercive inequalities on Carnot groups and applications 291
  21. On exponential Yang–Mills fields and p-Yang–Mills fields 317
  22. Index 359
https://doi.org/10.1515/9783110741711-018

Kapitel in diesem Buch

  1. Frontmatter I
  2. Foreword V
  3. Contents VII
  4. Hardy spaces associated to the Kohn Laplacian on a family of model domains in Cn+1 1
  5. Affine mixed Rayleigh quotients 29
  6. Riesz potentials and Hardy–Morrey spaces 49
  7. A conjecture regarding compact Lie groups and its consequences 79
  8. The singular Fredholm integral operators and related integral equations of Chandrasekhar type 89
  9. Extended multichannel weighted Schatten p-norm minimization for color image denoising 105
  10. The boundedness of a bilinear oscillatory integral 123
  11. On sharp Sobolev-type inequalities for multidimensional Cauchy measures 135
  12. Banach lattice-valued q-variation and convexity 153
  13. Weighted boundedness of Marcinkiewicz integral operators and related singular integral operators 167
  14. A spectral comparison note 195
  15. On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds 207
  16. The Neumann problem for the Laplacian in half-spaces 219
  17. An inequality on the mass of image of rectifiable chain under Lipschitz map 253
  18. Boundedness of general alternative Gaussian singular integrals on Gaussian variable Lebesgue spaces 261
  19. Remarks on weak–strong uniqueness for two-fluid model 281
  20. Coercive inequalities on Carnot groups and applications 291
  21. On exponential Yang–Mills fields and p-Yang–Mills fields 317
  22. Index 359
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