<a href="https://www.thenationalnews.com/tags/daniil-medvedev/" target="_blank">Daniil Medvedev</a> said after his previous two rounds at the Dubai Duty Free Tennis Championships that he would need to keep improving if he was to successfully defend his title. On Thursday in the quarter-finals, the improvement was evident as the top seed eased past Alejandro Davidovich Fokina 6-2, 6-3 with his best performance of the week so far. Before Dubai, Medvedev had not played since <a href="https://www.thenationalnews.com/sport/tennis/2024/01/28/jannik-sinner-battles-back-against-daniil-medvedev-to-claim-australian-open-title/" target="_blank">losing the Australian Open final</a> to Jannik Sinner a month ago, so a lack of match sharpness was hardly surprising. The Russian had to grind past Alexander Shevchenko and Lorenzo Sonego in the first and second rounds respectively but enjoyed a far more comfortable outing against eighth seed Davidovich Fokina to reach the semi-finals. Medvedev was not fully back to his brilliant best, although there was enough on show to suggest that he is trending in the right direction and remains the man to beat in Dubai. "Alejandro can play very well," Medvedev, 28, said. "Sometimes during matches he can have a little down moment and then he goes up. I knew that no matter the score, I needed to go until the last point. The second set at one moment got a bit tighter but I managed to stay there and win some more games and it was enough to win." The world No 4 set himself up for victory with a run that started towards the end of the first set and concluded midway through the second when he won seven straight games. After fending off three break points to hold for a 3-2 lead, Medvedev secured back-to-back breaks of his own to ease to a one-set lead in 36 minutes. The top seed maintained that momentum by racing into a 4-0 lead in the second set as he served and returned superbly, forcing Davidovich Fokina into errors and winning the majority of rallies. Medvedev's charge was unexpectedly halted when the Spaniard claimed one of the breaks back, but the damage was already done by that stage. As both players held for the remainder of the match, Medvedev clinched the victory with an unreturnable serve after 78 minutes on court. It was a far more composed and efficient performance from Medvedev, who admitted after Wednesday's win over Sonego that he <a href="https://www.thenationalnews.com/sport/tennis/2024/02/28/very-nervous-medvedev-beats-sonego-to-keep-dubai-title-defence-alive/" target="_blank">felt "very nervous"</a>. "I was feeling better," Medvedev said. "I don't know what happened yesterday. A few people around me got a small virus, so maybe it is this. Some days that happens but I am happy today happened. I am not at my best shape yet but we have some more matches." Through to the semi-finals, Medvedev keeps alive his hopes of defending a title for the first time in his career. To achieve that, he may have to defeat close friend Andrey Rublev in the final again after the second seed booked his place in the last four at the opposite end of the draw. Rublev, the 2022 Dubai champion, was in control of his earlier quarter-final match against Sebastian Korda when the American retired injured. The Russian world No 5 was leading by a set and a break 6-4, 4-3. "Today the game was not very good, but not because of the level. The conditions were super tough. It was really windy, a lot of sun with the shadow on the court," Rublev, 26, said. "When it's these kinds of conditions, the tennis is always not that beautiful, but you need to find a way. "You have to accept that this is the way it is. Sometimes today I was lucky as well because of those conditions. In important moments the ball moved because of the wind and he couldn't play well. It helped me a lot today." Rublev admitted he was surprised by Korda's retirement as there was no indication that the world No 33 was struggling with an injury or any physical limitations. With the Indian Wells Masters starting next week, there is a chance Korda was being precautious, although there has been no confirmation on the extent of his injury. "I didn't realise until the moment he told me he was finishing, because he was serving quite hard, he was hitting quite hard the ball," Rublev said. "I didn't notice any of the problem during the match. It was only when he told me he was finishing." Rublev will play Alexander Bublik for a place in the final after the Kazakh seventh seed also benefitted from an early retirement by his opponent. Leading 6-4, 4-1 Bublik booked his place in the semi-finals when Cezch world No 36 Jiri Lehecka called time on their match.