use File::Find::Rule;

my $start = '20110106';

my $dir   = '/path/to/dir/with/log/files/';
my @files = File::Find::Rule->file->name( 'meinDat_*.log' )->in( $dir );

my @wanted;
for my $file ( @files ) {
    my ($date) = $file =~ /meinDat_(\d{4}\.\d\d\.\d\d)\.log/;
    $date =~ s/\.//g;

    next if $date < $start;
    push @wanted, $file;
}

use Data::Dumper;
print Dumper \@wanted;