Orlicz dual affine quermassintegrals
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Chang-Jian Zhao
Abstract
In the paper, our main aim is to generalize the dual affine quermassintegrals to the Orlicz space.
Under the framework of Orlicz dual Brunn–Minkowski theory, we introduce a new affine
geometric quantity by calculating the first-order variation of the dual affine quermassintegrals, and call it the Orlicz dual affine quermassintegral.
The fundamental notions and conclusions of the dual affine quermassintegrals and the Minkoswki and Brunn–Minkowski inequalities for them are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual mixed volumes are also included in our conclusions.
The new Orlicz–Minkowski and Orlicz–Brunn–Minkowski inequalities in a special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn–Minkowski inequality, which also imply the
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11371334
Funding statement: Research is supported by National Natural Science Foundation of China (11371334).
Acknowledgements
The author expresses his thanks to the referee for his excellent suggestions and comments. The author expresses also his gratitude to the copy editor for reading the manuscript carefully and giving many wonderful suggestions about the language.
References
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Articles in the same Issue
- Frontmatter
- Distinct distances between points and lines in 𝔽q2
- A global perspective to connections on principal 2-bundles
- Integral group rings of solvable groups with trivial central units
- Lefschetz property and powers of linear forms in 𝕂[x,y,z]
- On quasi-convex null sequences in infinite cyclic groups
- On autocommutators and the autocommutator subgroup in infinite abelian groups
- Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms
- Finite-dimensional representations of Leavitt path algebras
- Orlicz dual affine quermassintegrals
- Universal locally finite maximally homogeneous semigroups and inverse semigroups
- Von Neumann algebras, L-algebras, Baer *-monoids, and Garside groups
- Boundedness and compactness of Hardy-type integral operators on Lorentz-type spaces
- A shifted convolution sum for \mathrm{GL}(3) × \mathrm{GL}(2)
- Equivariant Gauss sum of finite quadratic forms
- Right 2-Engel elements, central automorphisms and commuting automorphisms of Lie algebras
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Solution of Brauer’s
