N Ezekiel 25:12 - 14 we read a brief prophecy of judgment against the descendants of Esau. Here in Ezekiel 35 (and part of Ezekiel 36) we are confronted with a more expanded prophecy aimed at those same people. The Edomites lived to the southeast of Palestine. Today, the southern part of Jordan includes the same territory that was once inhabited by the children of Jacob's brother. After being occupied continually for about 1000 years, the famous city of Petra (named thusly because it was literally carved out of rock), now stands empty within this region, a symbol of the judgment of God on the people of that land.
The Edomites were obviously guilty of kicking their cousins while they were down (Ezekiel 35:5, 12 & 15). This angered God immensely and earned for the Edomites the wrath which is delineated in this section of Ezekiel. Beyond their infractions against the Jews, the Edomites were also guilty of blunt blasphemy (Ezekiel 35:13) and of infringing into territory (Samaria and Judah) where God Himself was rightfully dwelling (Ezekiel 35:10).
So, both in geography and in family relations, the Edomites were close to the city of God. But, because of their attitude and actions, they would have been better off if they had lived on the opposite side of the globe. Their close proximity to God's people only provided more opportunities for them to increase their violations against the God of Israel.