(Mishnah): One may not make a cavity underneath a public domain.

Similarly, one may not make pits, long pits or roofed pits under a public domain. R. Eliezer permits it as long as it is strong enough for a carriage carrying stones to ride over it.

One may not build beams or balconies out into the public domain. If he wishes to build them, he must do so within his own property.

If a person bought a courtyard that already had beams or balconies protruding into the public domain, they can remain this way.

(Gemara): If those pre-existing beams or balconies fell down and he wishes to rebuild them...

R. Yochanan: He has waived his right to them and he may not rebuild them.

Reish Lakish: He has not waived his right to them and he may rebuild them.

Each have a Beraisa that supports them....

Beraisa that supports R. Yochanan: If a person had a public path passing through his property and he took it and gave them a path on the side instead, the path on the side remains theirs but he cannot keep the first path.

Beraisa that supports Reish Lakish: If a person bought a courtyard that had beams or balconies protruding from it, if they fell, he may rebuild them.