The Brunn–Minkowski inequality for volume differences
نویسندگان
چکیده
منابع مشابه
The Width-volume Inequality
We prove that a bounded open set U in R n has k-width less than C(n) Volume(U) k/n. Using this estimate, we give lower bounds for the k-dilation of degree 1 maps between certain domains in R n. In particular, we estimate the smallest (n-1)-dilation of any degree 1 map between two n-dimensional rectangles. For any pair of rectangles, our estimate is accurate up to a dimensional constant C(n). We...
متن کاملa cauchy-schwarz type inequality for fuzzy integrals
نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.
15 صفحه اولA Volume Inequality for Polar Bodies
A sharp affine isoperimetric inequality is established which gives a sharp lower bound for the volume of the polar body. It is shown that equality occurs in the inequality if and only if the body is a simplex. Throughout this paper a convex body K in Euclidean n-space Rn is a compact convex set that contains the origin in its interior. Its polar body K∗ is defined by K∗ = {x ∈ R : x · y ≤ 1 for...
متن کاملA diamagnetic inequality for semigroup differences
The diamagnetic inequality for the magnetic Schrödinger semigroup is extended to the difference of the semigroups of magnetic Schrödinger operators with Neumann and Dirichlet boundary conditions on arbitrary open domains and rather general magnetic vector potentials A and potentials V . In particular, this bound renders moot all the technical issues in the recent proofs of the independence of t...
متن کاملSex Differences in the Association of Household Income with Amygdala Volume
Background: Household income and other socioeconomic position (SEP) indicators are among the most salient social determinants of children’s emotions and behaviors. Some research has shown that income and other SEP indicators may have certain sex-specific effects on the structures and functions of particular brain regions. Objectives: To investigate sex differences in the association of househ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2004
ISSN: 0196-8858
DOI: 10.1016/s0196-8858(03)00095-2