# Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

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### Orbifolds are Thom-Mather stratified spaces

Where can I find a proof of (or if it is even true) that an (effective) orbifold is a Thom-Mather stratified space? edit: after some search, I found the proof should be contained in either GIBSON, C....
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### Elliptic regularity when the Lagrangian is possibly infinite

I want to solve variational problems of the form $$\inf_u \int_{-1}^1 \phi(u'(x)) \text{ with } u(-1)=u(1) = 0,$$ where $\phi(p)$ is convex and is allowed to take on the value $+\infty$ for some ...
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### Direct calculation of the Fisher distance via Riemannian geodesics

I'm looking for a reference for a direct calculation of the Fisher distance (to avoid overloading the term "metric") $d_F(x,y) := 2 \cos^{-1} \sum_i \sqrt{x_i y_i}$ as the geodesic distance ...
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It is well known that the Riemann Hypothesis implies the following: $|\theta(x) - x| = O(x^{1/2 + \epsilon})$ for all $\epsilon > 0$. where $\theta$ is the first Chebyshev function; that is, $\... 1answer 83 views ### Change of variable and boundary data for Laplace equation Let us consider a smooth bounded domain$\Omega \subset \mathbb R^n$and the problem $$\begin{cases} -\Delta u = 0 & x \in \Omega \\ u = 1 & x \in \partial \Omega \end{cases}$$ Does it make ... 1answer 235 views ### Analogue of the second Hardy-Littlewood conjecture for numbers of divisors? Let$f(n)$denote the proposition "There exists some$k>1$such that $$\sum_{m=k}^{k+n-1}\tau(m) < \sum_{m=1}^n\tau(m)$$ where$\tau(m)$is the number of the divisors of$m$." (This ... 0answers 128 views ### de Rham currents/distributions on manifolds with boundaries My main source for currents and distribution theory on manifolds in general is de Rham's Differentiable Manifolds. To recap, let$M$be a smooth,$m$dimensional real manifold without boundary. De ... 1answer 154 views ### Viscosity solutions of$(-\Delta)^s u = 0$in$\Omega $with non-homogeneous data$u = 1$in$\mathbb R^n \setminus \Omega$Let us consider a smooth bounded domain$\Omega \subset \mathbb R^n$and the problem$$(1) \quad \begin{cases} (-\Delta)^s u +\lambda u= 0 & x \in \Omega \\ u = 1 & x \in \mathbb R^n \... 0answers 45 views ### Second order estimates for Dirichlet problem for complex Monge-Ampere equation Let$\Omega\subset \mathbb{C}^n$be a bounded pseudo-convex domain. Let$0<f\in C^{\infty}(\bar\Omega)$,$\phi\in C^\infty(\partial \Omega)$. Consider the Dirichlet problem for the complex Monge -... 0answers 74 views ### "Dual" of a CP map Let$M,N$be von Neumann algebras, and let$\phi:M\rightarrow N$be a normal completely positive map. I am interested in conditions when there is a "dual" normal completely positive map$\...
A standard fact that underlies the Fenchel-Nielsen coordinates on Teichmuller space is the fact that for all triples $(a,b,c)$ of positive real numbers, there exists a unique hyperbolic hexagon whose ...