The phrase
"slender margin" means a very small or narrow difference or gap between two things.
Full definition
It was their tendency during qualifying to win
by slender margins but win they did and Italy amassed a very healthy 24 points from qualification.
Having achieved a renewed mandate — albeit by
a slender margin in the popular vote — and with the devastation wrought by hurricane Sandy fresh in the memory, Obama may be well placed to seize the moment.
On leading the championship by
a slender margin... «It's getting down to the business end of the year.
And I think most reviewers would agree that the HTC U11 has, by
a slender margin, probably the best phone camera released in 2017 to date.