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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

3 votes
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255 views

Sobolev type inequalities involving affine metric

Let $\mathcal{M}$ be a compact smooth hypersurface in $\mathbb{R}^{n}$ with affine metric $h$ and affine volume measure $d\mu_{h}$. If $$\int_{\mathcal{M}}|\nabla f|^2_{h}d\mu_{h}$$ is small what can …