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An inequality on the mass of image of rectifiable chain under Lipschitz map
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Chunyan Liu
Abstract
For a complete normed abelian group G, we show that the mass of image of a rectifiable G-chain S under chain map f♯ induced by Lipschitz map f is controlled by the integral of Jacobian of f restricted on the support of S with respect to the associated radon measure μS.
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Abstract
For a complete normed abelian group G, we show that the mass of image of a rectifiable G-chain S under chain map f♯ induced by Lipschitz map f is controlled by the integral of Jacobian of f restricted on the support of S with respect to the associated radon measure μS.
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Chapters in this book
- Frontmatter I
- Foreword V
- Contents VII
- Hardy spaces associated to the Kohn Laplacian on a family of model domains in Cn+1 1
- Affine mixed Rayleigh quotients 29
- Riesz potentials and Hardy–Morrey spaces 49
- A conjecture regarding compact Lie groups and its consequences 79
- The singular Fredholm integral operators and related integral equations of Chandrasekhar type 89
- Extended multichannel weighted Schatten p-norm minimization for color image denoising 105
- The boundedness of a bilinear oscillatory integral 123
- On sharp Sobolev-type inequalities for multidimensional Cauchy measures 135
- Banach lattice-valued q-variation and convexity 153
- Weighted boundedness of Marcinkiewicz integral operators and related singular integral operators 167
- A spectral comparison note 195
- On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds 207
- The Neumann problem for the Laplacian in half-spaces 219
- An inequality on the mass of image of rectifiable chain under Lipschitz map 253
- Boundedness of general alternative Gaussian singular integrals on Gaussian variable Lebesgue spaces 261
- Remarks on weak–strong uniqueness for two-fluid model 281
- Coercive inequalities on Carnot groups and applications 291
- On exponential Yang–Mills fields and p-Yang–Mills fields 317
- Index 359
Chapters in this book
- Frontmatter I
- Foreword V
- Contents VII
- Hardy spaces associated to the Kohn Laplacian on a family of model domains in Cn+1 1
- Affine mixed Rayleigh quotients 29
- Riesz potentials and Hardy–Morrey spaces 49
- A conjecture regarding compact Lie groups and its consequences 79
- The singular Fredholm integral operators and related integral equations of Chandrasekhar type 89
- Extended multichannel weighted Schatten p-norm minimization for color image denoising 105
- The boundedness of a bilinear oscillatory integral 123
- On sharp Sobolev-type inequalities for multidimensional Cauchy measures 135
- Banach lattice-valued q-variation and convexity 153
- Weighted boundedness of Marcinkiewicz integral operators and related singular integral operators 167
- A spectral comparison note 195
- On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds 207
- The Neumann problem for the Laplacian in half-spaces 219
- An inequality on the mass of image of rectifiable chain under Lipschitz map 253
- Boundedness of general alternative Gaussian singular integrals on Gaussian variable Lebesgue spaces 261
- Remarks on weak–strong uniqueness for two-fluid model 281
- Coercive inequalities on Carnot groups and applications 291
- On exponential Yang–Mills fields and p-Yang–Mills fields 317
- Index 359
