How well supported is the generic interpretation Rublev's Icon as being a depiction of the Holy Trinity as portrayed in Genesis 18? This was produced in the 15th century by Andrei Rublev's icon of the Trinity, a highly regarded Russian orthodox artist:



It is generally taken to be depicting the three men of Genesis 18 as being physical visitations of the Godhead.

Are there any texts from authoritative commentaries, the early church fathers, theologians or research that support Rublev's depicted interpretation of this passage?

Different denominations may have differing views so please quote your source references.
Among church fathers, Ambrose is one supporter:


  Abraham, who was glad to receive strangers, faithful to God and tireless in his service and prompt in fulfilling his duty, saw the Trinity typified.  He added religious devotion to hospitality, for although he beheld three, he adored one, and while keeping a distinction of the persons, yet he called one Lord, thus giving honor to the three but signifying one power. (On His Brother, Satyrus 2.96)


Caesarius of Arles similarly writes:


  He received the three men and served them loaves out of three measures.  Why is this, brothers, unless it means the mystery of the Trinity? [...] In the fact that he saw three, as was already said, he understood the mystery of the Trinity, but since he adored them as one, he recognized that there is one God in three persons. (Sermon 83.4)


Origen actually finds images of the members of the Trinity in the food that is served.  The calf represents Christ (Homilies on Genesis 4.2), and the preparation of three equal measures of flour into bread is an image of the Trinity (On Abraham 1.5.38).

Other fathers are not so supportive of this idea.  Ephrem the Syrian believed just one of them was the Lord (Commentary on Genesis, 15.1), while Augustine called all three of them angels (City of God, 16.29).

See the Ancient Christian Commentary if you'd like to investigate further.