Photo source: "Ingdalsboka" by Anders Aune (Gunerius' son)
Martin and Gunerius were the sons of Peder Pedersen (alternative spelling Per Persson; 1836-1916) from the croft Bjørnbethåggån or Hesthåggån in the neighboring village of Geitastranda. Peder had been living alone with his aging mother (Maret Evensdatter Geitaneset 1791-1872) in this tiny seaside village for years, eking out a meager subsistence as a fisherman. In 1870, however, he moved to Grostadgjerdet/Aunet, where his older sister had lived earlier. Peder then became known locally as "Per Aune", using the name of his residence as a surname, as was the custom at the time.
Two years later, Peder married Ane Olsdatter Rian (1845-1932), and the couple had four children, all sons; the youngest, Andreas, died as a child, while the oldest, Peder Odin, emigrated to America. My great-great-grandfather Martin moved to the city of Trondheim around the year 1898, so it was Gunerius, the youngest surviving son, who continued to run the family croft. Today, Aunet is still owned by Gunerius' descendants, but the land has been leased away, and the house is now used only as a vacation home.
Gunerius' descendants still use Aune as their surname. The surname Aune (without a t) is the indefinite form of the word; the t in the place name Aunet is a neuter singular definite article (equivalent to the English word "the"). I don't know why different grammatical forms are used for the place name and the surname, but the practice has become tradition now, and is not likely to change.