So, I have tried it with your suggestions, but did not get the expected result.
Luckily one of our developers came and helped me to write this:
$mydate = $page->week_begin;
$mydateArray = explode('.', $mydate);
foreach ( $mydateArray as $index => $nummer ) {
$mydateArray[$index] = ltrim($nummer, '0');
}
$timestamp = mktime(0, 0, 0, $mydateArray[1], $mydateArray[0], $mydateArray[2]);
$dateObj = new \DateTime(date('Y-m-d', $timestamp));
$dateObj->modify('+6 days');
echo $dateObj->format('d.m.Y');
Which works fine for me.
Thank you anyway!