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# All Questions

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### How many singular values are there for this function on Stiefel manifold

Let $\mathcal{M}=\{X\in\mathbb{R}^{n\times r}: X^TX=I\}$ and define a function $f$ on $\mathcal{M}$: $$f(X)=\sum_{i=1}^n\left(\sum_{j=1}^rv_jX_{ij}^2\right)^2$$ where $(v_1,...,v_r)$ is some unit ...
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### Covariant derivative of the Monge-Ampere equation on Kähler manifolds

I am reading D. Joyce book "Compact manifolds with special holonomy" and I have some problems of understanding some computation on page 111, the first line in the proof of Proposition 5.4.6. More ...
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### Laplacian spectrum asymptotics in neck stretching

Let $M$ be a compact Riemannian manifold. Let $S \subset M$ be a smooth hypersurface separating $M$ into two components. Let $g_T$ be a family of Riemannian metric obtained by stretching along $S$, i....

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