Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Franz E. Schuster"'
Autor:
Franz E. Schuster, Georg C. Hofstätter
Publikováno v:
International Mathematics Research Notices. 2023:1378-1419
It is shown that each monotone Minkowski endomorphism of convex bodies gives rise to an isoperimetric inequality, which directly implies the classical Urysohn inequality. Among this large family of new inequalities, the only affine invariant one—th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e8dbf7a8466afe4d66ca6d2574ae2fab
https://doi.org/10.1093/imrn/rnab262
https://doi.org/10.1093/imrn/rnab262
Autor:
Oscar Ortega-Moreno, Franz E. Schuster
It is shown that for any sufficiently regular even Minkowski valuation $\Phi$ which is homogeneous and intertwines rigid motions, there exists a neighborhood of the unit ball, where balls are the only solutions to the fixed-point problem $\Phi^2 K =
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8943782382d0677fc7832877085a5e8c
Autor:
Thomas Wannerer, Franz E. Schuster
Publikováno v:
Journal of the European Mathematical Society. 20:1851-1884
A convolution representation of continuous translation invariant and SO(n) equivariant Minkowski valuations is established. This is based on a new classification of translation invariant generalized spherical valuations. As applications, Crofton and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d0938d2e125bfa648d072275b8eb5dd3
https://doi.org/10.4171/jems/801
https://doi.org/10.4171/jems/801
Autor:
Franz E. Schuster, Felix Dorrek
Publikováno v:
Journal of Functional Analysis. 273:2026-2069
Dual to Koldobsky's notion of j -intersection bodies, the class of j -projection bodies is introduced, generalizing Minkowski's classical notion of projection bodies of convex bodies. A Fourier analytic characterization of j -projection bodies in ter
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1b10ece1572bb36166bdf3ef38873799
https://doi.org/10.1016/j.jfa.2017.06.003
https://doi.org/10.1016/j.jfa.2017.06.003
Autor:
Astrid Berg, Franz E. Schuster
Publikováno v:
Journal of Mathematical Analysis and Applications. 490:124190
Lutwak's volume inequalities for polar projection bodies of all orders are generalized to polarizations of Minkowski valuations generated by even, zonal measures on the Euclidean unit sphere. This is based on analogues of mixed projection bodies for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0a505b8e9dd7a520cea2462945410dd6
https://doi.org/10.1016/j.jmaa.2020.124190
https://doi.org/10.1016/j.jmaa.2020.124190
Autor:
Philipp Kniefacz, Franz E. Schuster
Publikováno v:
Journal of Geometric Analysis
A family of sharp $L^p$ Sobolev inequalities is established by averaging the length of $i$-dimensional projections of the gradient of a function. Moreover, it is shown that each of these new inequalities directly implies the classical $L^p$ Sobolev i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3a346e885bea9f3d69547791a8451fe1
Autor:
Franz E. Schuster, Thomas Wannerer
Publikováno v:
American Journal of Mathematics. 137:1651-1683
A new integral representation of smooth translation invariant and rotation equivariant even Minkowski valuations is established. Explicit formulas relating previously obtained descriptions of such valuations with the new more accessible one are also
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::87086841a9d00b9ad2493e5312646c4b
https://doi.org/10.1353/ajm.2015.0041
https://doi.org/10.1353/ajm.2015.0041
Autor:
Christoph Haberl, Franz E. Schuster
Publikováno v:
Advances in Mathematics. 356:106811
It is shown that every even, zonal measure on the Euclidean unit sphere gives rise to an isoperimetric inequality for sets of finite perimeter which directly implies the classical Euclidean isoperimetric inequality. The strongest member of this large
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21daea18d14243675c53330988794f11
https://doi.org/10.1016/j.aim.2019.106811
https://doi.org/10.1016/j.aim.2019.106811
Publikováno v:
Oberwolfach Reports. 10:295-342
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7e102f7fc1c7bcdc17aa1a61fc0aafe9
https://doi.org/10.4171/owr/2013/05
https://doi.org/10.4171/owr/2013/05
Autor:
Lukas Parapatits, Franz E. Schuster
Publikováno v:
Advances in Mathematics
A Steiner type formula for continuous translation invariant Minkowski valuations is established. In combination with a recent result on the symmetry of rigid motion invariant homogeneous bivaluations, this new Steiner type formula is used to obtain a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eb698cb1480e4c6c093b32a87fc8d827
https://doi.org/10.1016/j.aim.2012.03.024
https://doi.org/10.1016/j.aim.2012.03.024