1. Reduce space above and below equations: Place following lines after \begin{document}
\setlength{\abovedisplayskip}{2pt}
\setlength{\belowdisplayskip}{2pt}

2.  Reduce space above and below section/subsection titles. Place these lines before beginning the document.

\usepackage[compact]{titlesec}
\titlespacing*{\section} {0pt}{2\baselineskip}{3\baselineskip}
\titlespacing*{\subsection} {0pt}{2\baselineskip}{3\baselineskip}

This answer is copied from this StackOverflow link. In Springer, llncs format I found this sucks but a hack around the same is provided in this StackOverflow answer. It really works!!.