## Tagged Questions

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### Hyperbolic pair of pants.

Suppose $Y$ is a pair of pants with a hyperbolic structure and $\gamma_i; i = 1, 2, 3$ are the geodesic boundaries of length $l_i; i=1, 2, 3$ respectively. Now consider a essential …
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### G-equivariant Whitehead’s Theorem

Suppose $X$ is a CW complex and $Y$ is a subcomplex. Let $G$ be a compact Lie group that acts on $X$ and $Y$. Suppose further that the CW structures on $X$ and $Y$ are $G$-stable …
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### A family of words counted by the Catalan numbers

In recent work with Michael Albert and Nik Ruškuc, a family of words has arisen which is counted by the Catalan numbers. I've looked at Richard Stanley's Catalan exercises in EC2 a …
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### Solution formular for Laplace equation

I want to slove the Laplace equation on $R^3_+$ with Neumann boundary condition. The equation reads: $-\Delta u = f$ in $R^3_+$, $\partial_3 u|_{x_3=0}=g$ on $R^2$. If $f$, $g$ sa …
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### Is there anyway to rewrite a partial differential equation using language of differential forms, tensors,.etc

My question is: usually, a partial differential equation, for example, those coming from physics, is written in a lauguage of vector calculus in a local coordinate, is there anyway …
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### PDE with the Jacobian Determinant

Hello, Could you please help me in answering the following question? Initially I thought that the following problem can be solved through Monge-Ampere equation, but with Monge-Am …
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### Growth of Thompson’s group $F$

EDIT: Mark Sapir pointed a reference (in the comments) giving a lower bound of $2^{1/4}$ for the minimal rate. Is this the state of art? The third question remains unanswered. If …
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### Permutation and Combination question… [closed]

Hello, I am currently studying Extension 1 Mathematics. I missed two classes and I figured out that tomorrow I will have a quiz. Can you help me to solve this permutation and combi …
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### A question about $L^p$ integral of an entire function on $\mathbb{C}$

Question: Suppose that $f$ is an entire function (i.e. analytic in $\mathbb{C}$), and satisfies the condition $\iint_{\mathbb{C}}|f|^p dxdy<\infty$ for some $p\in (0,1)$. I gues …
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### Is there a good reason why a^{2b} + b^{2a} <= 1 when a+b=1?

The following problem is not from me, yet I find it a big challenge to give a nice (in contrast to 'heavy computation') proof. The motivation for me to post it lies in its concise …