In The Bet, why does the lawyer's letter state "burn or freeze together with the earthly globe?"
The quote that you are referring to is from Anton Chekhov's short story "The Bet." The story has a simple enough premise. A lawyer and a banker are having an argument. The banker argues that capital punishment is more humane, and the lawyer argues that life in prison is more humane. The lawyer's point is that any life is better than no life at all.
"Capital punishment and life-imprisonment are equally immoral; but if I were offered the choice between them, I would certainly choose the second. It's better to live somehow than not to live at all."
The banker and lawyer argue a bit more about it, and the banker offers up his bet. He bets 2 million rubles that the lawyer won't last five years in solitary confinement. The lawyer ups the bet to fifteen years. Why? The story doesn't say.
The lawyer is one day away from winning the bet, and the banker is not happy about it. He decides to kill the lawyer in order to keep his money. Upon entering the room, the banker finds a note written by the lawyer. The note says that he intends to throw the bet five minutes early, because he is disgusted with all mankind. He doesn't want the money. The line that your question asks about is as follows:
Though you be proud and wise and beautiful, yet will death wipe you from the face of the earth like the mice underground; and your posterity, your history, and the immortality of your men of genius will be as frozen slag, burnt down together with the terrestrial globe.
The lawyer has learned a lot from the books that he read during his fifteen years of imprisonment. His letter states that while mankind has produced some amazing people, literature, and art, all of it will die and fade away. All of it will come to an end. The frozen and burnt part is simply a concrete way of saying how mankind's achievements will be destroyed when the Earth is destroyed. The letter is a depressing read.