The -Minkowski problem with super-critical exponents
The $ L_p $-Minkowski problem deals with the existence of closed convex hypersurfaces in
$\mathbb {R}^{n+ 1} $ with prescribed $ p $-area measures. It extends the classical
Minkowski problem and embraces several important geometric and physical applications.
The Existence of solutions has been obtained in the sub-critical case $ p>-n-1$, but the
problem remains widely open in the super-critical case $ p<-n-1$. In this paper, we
introduce new ideas to solve the problem for all the super-critical exponents. A crucial …
$\mathbb {R}^{n+ 1} $ with prescribed $ p $-area measures. It extends the classical
Minkowski problem and embraces several important geometric and physical applications.
The Existence of solutions has been obtained in the sub-critical case $ p>-n-1$, but the
problem remains widely open in the super-critical case $ p<-n-1$. In this paper, we
introduce new ideas to solve the problem for all the super-critical exponents. A crucial …
The -Minkowski problem deals with the existence of closed convex hypersurfaces in with prescribed -area measures. It extends the classical Minkowski problem and embraces several important geometric and physical applications. The Existence of solutions has been obtained in the sub-critical case , but the problem remains widely open in the super-critical case . In this paper, we introduce new ideas to solve the problem for all the super-critical exponents. A crucial ingredient in our proof is a topological method based on the calculation of the homology of a topological space of ellipsoids.
arxiv.org
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