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Results tagged with geometric-analysis
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user 3948
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Finding constant curvature metrics on surfaces for the case of positive Euler characteristic
Try looking in Alice Chang's ETH notes. Chapters 1 and 2 deals with the prescribed Gaussian curvature equation in 0 and positive Euler characteristics. Presumeably there's some mention of where you ca …
- 39.1k
7
votes
Accepted
Completeness hypothesis in the positive mass theorem
Completeness is necessary. Otherwise you can just take a maximal spatial slice of the negative-mass Schwarzschild solution (i.e. a constant $t$ slice in Boyer-Lindquist coordinates) and it has vanishi …
- 39.1k
2
votes
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Solvability of $u_t=\nabla_{u_\theta} u_\theta -\frac{1}{2}\nabla R +\frac{1}{2\tau}u_\theta...
In Ottarsson's paper that you cited the curves are by definition closed, that is, they are images of $\mathbb{S}^1$. In Cao and Zhu, the $\mathcal{L}$-geodesics must be "open" in the sense that they …
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5
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Derive distributional inequalities from pointwise estimates
First note that the result is true if the support of $\varphi$ is disjoint from $E$; this follows from integration by parts.
Next note that every algebraic set is a finite union of smooth submanifolds …
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