(a) The Gemara says in Perek Hazorek that if you had an arch, you don't need a Mezuzah. Everyone agrees that if it was 10 Tefachim high and then it got round, it does need a Mezuzah, but then the Gemara asks, "what if it was like this?", then there is a Machlokes. One opinion is you have to put a Mezuzah there and the other opinion is you don't. My question is why can't you say Lovud at the top so you don't have to put a Mezuzah there ?
(b) I've got another question. The Mezuzah has to go in the top 3rd of the doorpost, so if you have any of those doorways, , where do you calculate the top third, where does the doorway start. Does the Mezuzah go on the red line here, or the red line here ?
(a) The Ritva in Yoma 11b quotes Rishonim who agree with you that if the two
doorposts are less than three Tefachim apart at any point in the ten
Tefachim required to make the door, even Rebbi Meir agrees that the door
does not need a Mezuzah. However, it appears from the Ritva that this is not
a matter that is beyond debate. I would suggest that others may argue that
if we have three Tefachim high by four wide at the base of the door this is
enough of a Pesach for us to say Chokekim le'Hashlim (according to Rebbi
Meir) even if the rest of the door is not three wide, as long as it is ten
high.
(b) The Mezuzah would be placed above two thirds of the whole height of the
door since the entire opening is considered to be a Pesach.
Dov Freedman