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A final involving former US Open champions Medvedev and three-time winner Novak Djokovic on Sunday is one of obvious high quality but not the next chapter in tennis's hottest rivalry of Djokovic and Alcaraz that has had the sport buzzing.
Alcaraz defeated a drained Alexander Zverev 6-3 6-2 6-4 on Wednesday.
On another steamy hot day with temperatures in the mid-90s Fahrenheit (32 Celsius) Medvedev was better able deal with the stifling humidity and heat inside Arthur Ashe Stadium than eighth seed Rublev to make the Flushing Meadows semi-finals for the fourth time in five years.
Sabalenka faces China's Zheng, who knocked out 2022 finalist Ons Jabeur, in the qusarterfinals.
New York: World No. 1 Carlos Alcaraz aced his first real test at the US Open on Saturday powering past Britain's Daniel Evans while women's second seed Aryna Sabalenka schooled France's Clara Burel to move into the fourth round of the year's final Grand Slam. There were also lessons learned about
The British charge at the US Open will carry on without 2012 champion Andy Murray, who was outclassed by Bulgarian Grigor Dimitrov.
Djokovic, who overwhelmed Alcaraz in the French Open semifinals last month, is bidding for a record-equalling eighth Wimbledon crown to become the oldest men's champion and match Margaret Court's all-time record of 24 Grand Slams.
The World No 1 defeated his childhood friend Holger Rune of Denmark in the quarterfinals.
Djokovic defeated Poland's Hubert Hurkacz 7-6(6) 7-6(6) 5-7 6-4.
Equalling his best ever showing at Wimbledon, Daniil Medvedev downed Hungary's Marton Fucsovics 4-6 6-3 6-4 6-4 to reach the fourth round.