\documentclass{article}
\usepackage{amsfonts}
\usepackage{pst-plot,pstcol,pst-node}
\pagestyle{empty}
\newpsobject{showgrid}{psgrid}{subgriddiv=1,griddots=10}
\begin{document}

%%\noindent 2 circles and a square
\begin{pspicture}(-4,-4)(4,4)\showgrid
\psset{xunit=1cm,yunit=1cm}
% Draw big circle
\pscircle(0,0){2}
% Draw square
\psframe[fillstyle=solid,fillcolor=darkgray]
	(-1.414,-1.414)(1.414,1.414)
% Draw small circle
\pscircle[fillstyle=solid,fillcolor=lightgray](0,0){1.414}
% Put in labels
\dotnode(0,0){C}
\rput(-.1,-.3){$B_1/\sqrt{2}$}
\rput(3,3){$\partial B_1\bigcap V$}
\rput(3,2.7){$dim_\mathbb{R}=2n-3$} 
\rput(4,0){$dim_\mathbb{R}=n$} 
% Draw arrows from labels to points
\pscurve{->}(3,2.5)(2.5,1.5)(1.414,1.414)
\psline{->}(3,0)(1.414,0)
\end{pspicture}

%% Draw two curves and fill in the area between them:
\begin{pspicture}(0,0)(4,4)\showgrid
\psset{xunit=1cm,yunit=1cm}
\psaxes[axesstyle=axes,labels=none,ticks=none](0,0)(0,4)(4,0)
\pscustom{%
\pscurve(0,1.6)(2,3)(3,2)(4,2.5)
\gsave
\pscurve[liftpen=1](4,2)(3,.2)(2,.5)(1,3)(0,.6)
\fill[fillstyle=crosshatch]
\grestore}
\pscurve[liftpen=2](4,2)(3,.2)(2,.5)(1,3)(0,.6)
\end{pspicture}

\end{document}