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Results tagged with dg.differential-geometry
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user 34154
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
4
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0
answers
102
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Minimal hypersurfaces with finite index and eigenvalues of the Laplacian
Let $M^n$ be a minimal hypersurface in $R^{n+1}$ with finite index. Can $\lambda_1(M^n)$ be a positive number? Are there examples of such hypersurfaces? (Even surfaces...)
Recall that $M^n$ has finit …
- 56
0
votes
0
answers
270
views
Gradient estimates for subsolutions of elliptic equations
Let $M$ be a Riemannian manifold. Assume $u \in C^\infty(M)$ such that $u>0$ and
$\Delta u + \lambda u = 0,$
where $\lambda \geq 0$. There is a poinwise estimate for $|\nabla u|$ in Peter Li's book …
- 56
0
votes
Estimates for Green's function
I don't know if this helps you...
Consider the warped product metric on $M^n = R \times S^{n-1}$
$ds^2 = dr^2 + f(r)^2 ds_{S^{n-1}}.$
Assume $u=u(r)$, where $r$ is the distance function from some f …
- 56
0
votes
Accepted