I have a document with some (very few) umlauts, for example:
\documentclass[11pt,a4paper]{article}
\begin{document}
This is the Hölder inequality:
$$
\Vert f g \Vert_1 \leq \Vert f \Vert_p \Vert g \Vert_q
$$
\end{document}
This almost works as I have the umlaut in the PDF. However, when I search in the PDF the name "Hölder", it is not found because of the umlaut.
I found the following solution:
\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\begin{document}
This is the Hölder inequality:
$$
\Vert f g \Vert_1 \leq \Vert f \Vert_p \Vert g \Vert_q
$$
\end{document}
The package \usepackage[T1]{fontenc} seems to fix the problem that umlauts are not searchable, the \usepackage{lmodern} seems to be necessary in order to get a high quality PDF.
So far so good, but somehow these packages seem to slightly change the font/spacing/captions (not really sure) used by Latex.
The problem is that if I include these packages into a large document, suddenly many pages are messed up because the content that previously fit on a single page now (for some obscure reason) needs more space. Just including these two packages increased the page count of my document by more than 10%. Rearranging everything is not an option.
Question: How can I have searchable umlauts with high PDF quality and exactly the same font/captions/distances/etc. like without them?